User:Hjilderda/differentiation

Een numerieke differentiatie formule is een formule voor de numerieke benadering van een afgeleide als gewogen som van functiewaarden in equidistante punten. De basisgedachte daarbij is de functie te benaderen door een polynoom en het benaderende polynoom exact te differentiëren.

Definitie
Gegeven is de op het interval [a,b] differentieerbare functie f. Het interval wordt opgedeeld in n deelintervallen van gelijke lengte:
 * $$a = x_0 < x_1 < \ldots < x_n = b$$

de stapgrootte:
 * $$h = \frac{b-a}{n} = x_i - x_{i-1},\quad i = 1,\ldots, n$$

en de functiewaarden:
 * $$f_i = f(x_i) = f(a + i h),\quad i = 0, 1,\ldots, n$$

2-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=-f_{0}+f_{1}-\frac{1}{2}h^{2}f^{(2)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=-f_{0}+f_{1}+\frac{1}{2}h^{2}f^{(2)}(\xi)$$

3-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{2}(-3f_{0}+4f_{1}-f_{2})+\frac{1}{3}h^{3}f^{(3)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{2}(-f_{0}+f_{2})-\frac{1}{6}h^{3}f^{(3)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{2}(f_{0}-4f_{1}+3f_{2})+\frac{1}{3}h^{3}f^{(3)}(\xi)$$

3-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=f_{0}-2f_{1}+f_{2}-h^{3}f^{(3)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=f_{0}-2f_{1}+f_{2}-\frac{1}{12}h^{4}f^{(4)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=f_{0}-2f_{1}+f_{2}+h^{3}f^{(3)}(\xi)$$

4-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{6}(-11f_{0}+18f_{1}-9f_{2}+2f_{3})-\frac{1}{4}h^{4}f^{(4)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{6}(-2f_{0}-3f_{1}+6f_{2}-f_{3})+\frac{1}{12}h^{4}f^{(4)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{6}(f_{0}-6f_{1}+3f_{2}+2f_{3})-\frac{1}{12}h^{4}f^{(4)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{6}(-2f_{0}+9f_{1}-18f_{2}+11f_{3})+\frac{1}{4}h^{4}f^{(4)}(\xi)$$

4-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=2f_{0}-5f_{1}+4f_{2}-f_{3}+\frac{11}{12}h^{4}f^{(4)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=f_{0}-2f_{1}+f_{2}-\frac{1}{12}h^{4}f^{(4)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=f_{1}-2f_{2}+f_{3}-\frac{1}{12}h^{4}f^{(4)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=-f_{0}+4f_{1}-5f_{2}+2f_{3}+\frac{11}{12}h^{4}f^{(4)}(\xi)$$

4-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=-f_{0}+3f_{1}-3f_{2}+f_{3}-\frac{3}{2}h^{4}f^{(4)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=-f_{0}+3f_{1}-3f_{2}+f_{3}-\frac{1}{2}h^{4}f^{(4)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=-f_{0}+3f_{1}-3f_{2}+f_{3}+\frac{1}{2}h^{4}f^{(4)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=-f_{0}+3f_{1}-3f_{2}+f_{3}+\frac{3}{2}h^{4}f^{(4)}(\xi)$$

5-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{12}(-25f_{0}+48f_{1}-36f_{2}+16f_{3}-3f_{4})+\frac{1}{5}h^{5}f^{(5)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{12}(-3f_{0}-10f_{1}+18f_{2}-6f_{3}+f_{4})-\frac{1}{20}h^{5}f^{(5)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{12}(f_{0}-8f_{1}+8f_{3}-f_{4})+\frac{1}{30}h^{5}f^{(5)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{12}(-f_{0}+6f_{1}-18f_{2}+10f_{3}+3f_{4})-\frac{1}{20}h^{5}f^{(5)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{12}(3f_{0}-16f_{1}+36f_{2}-48f_{3}+25f_{4})+\frac{1}{5}h^{5}f^{(5)}(\xi)$$

5-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{12}(35f_{0}-104f_{1}+114f_{2}-56f_{3}+11f_{4})-\frac{5}{6}h^{5}f^{(5)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{12}(11f_{0}-20f_{1}+6f_{2}+4f_{3}-f_{4})+\frac{1}{12}h^{5}f^{(5)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{12}(-f_{0}+16f_{1}-30f_{2}+16f_{3}-f_{4})+\frac{1}{90}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{12}(-f_{0}+4f_{1}+6f_{2}-20f_{3}+11f_{4})-\frac{1}{12}h^{5}f^{(5)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{12}(11f_{0}-56f_{1}+114f_{2}-104f_{3}+35f_{4})+\frac{5}{6}h^{5}f^{(5)}(\xi)$$

5-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{2}(-5f_{0}+18f_{1}-24f_{2}+14f_{3}-3f_{4})+\frac{7}{4}h^{5}f^{(5)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{2}(-3f_{0}+10f_{1}-12f_{2}+6f_{3}-f_{4})+\frac{1}{4}h^{5}f^{(5)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{2}(-f_{0}+2f_{1}-2f_{3}+f_{4})-\frac{1}{4}h^{5}f^{(5)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{2}(f_{0}-6f_{1}+12f_{2}-10f_{3}+3f_{4})+\frac{1}{4}h^{5}f^{(5)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{2}(3f_{0}-14f_{1}+24f_{2}-18f_{3}+5f_{4})+\frac{7}{4}h^{5}f^{(5)}(\xi)$$

5-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}-2h^{5}f^{(5)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}-h^{5}f^{(5)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}-\frac{1}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}+h^{5}f^{(5)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}+2h^{5}f^{(5)}(\xi)$$

6-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{60}(-137f_{0}+300f_{1}-300f_{2}+200f_{3}-75f_{4}+12f_{5})-\frac{1}{6}h^{6}f^{(6)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{60}(-12f_{0}-65f_{1}+120f_{2}-60f_{3}+20f_{4}-3f_{5})+\frac{1}{30}h^{6}f^{(6)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{60}(3f_{0}-30f_{1}-20f_{2}+60f_{3}-15f_{4}+2f_{5})-\frac{1}{60}h^{6}f^{(6)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{60}(-2f_{0}+15f_{1}-60f_{2}+20f_{3}+30f_{4}-3f_{5})+\frac{1}{60}h^{6}f^{(6)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{60}(3f_{0}-20f_{1}+60f_{2}-120f_{3}+65f_{4}+12f_{5})-\frac{1}{30}h^{6}f^{(6)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{60}(-12f_{0}+75f_{1}-200f_{2}+300f_{3}-300f_{4}+137f_{5})+\frac{1}{6}h^{6}f^{(6)}(\xi)$$

6-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{12}(45f_{0}-154f_{1}+214f_{2}-156f_{3}+61f_{4}-10f_{5})+\frac{137}{180}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{12}(10f_{0}-15f_{1}-4f_{2}+14f_{3}-6f_{4}+f_{5})-\frac{13}{180}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{12}(-f_{0}+16f_{1}-30f_{2}+16f_{3}-f_{4})+\frac{1}{90}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{12}(-f_{1}+16f_{2}-30f_{3}+16f_{4}-f_{5})+\frac{1}{90}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{12}(f_{0}-6f_{1}+14f_{2}-4f_{3}-15f_{4}+10f_{5})-\frac{13}{180}h^{6}f^{(6)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{12}(-10f_{0}+61f_{1}-156f_{2}+214f_{3}-154f_{4}+45f_{5})+\frac{137}{180}h^{6}f^{(6)}(\xi)$$

6-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{4}(-17f_{0}+71f_{1}-118f_{2}+98f_{3}-41f_{4}+7f_{5})-\frac{15}{8}h^{6}f^{(6)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{4}(-7f_{0}+25f_{1}-34f_{2}+22f_{3}-7f_{4}+f_{5})-\frac{1}{8}h^{6}f^{(6)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{4}(-f_{0}-f_{1}+10f_{2}-14f_{3}+7f_{4}-f_{5})+\frac{1}{8}h^{6}f^{(6)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{4}(f_{0}-7f_{1}+14f_{2}-10f_{3}+f_{4}+f_{5})-\frac{1}{8}h^{6}f^{(6)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{4}(-f_{0}+7f_{1}-22f_{2}+34f_{3}-25f_{4}+7f_{5})+\frac{1}{8}h^{6}f^{(6)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{4}(-7f_{0}+41f_{1}-98f_{2}+118f_{3}-71f_{4}+17f_{5})+\frac{15}{8}h^{6}f^{(6)}(\xi)$$

6-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=3f_{0}-14f_{1}+26f_{2}-24f_{3}+11f_{4}-2f_{5}+\frac{17}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=2f_{0}-9f_{1}+16f_{2}-14f_{3}+6f_{4}-f_{5}+\frac{5}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=f_{0}-4f_{1}+6f_{2}-4f_{3}+f_{4}-\frac{1}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=f_{1}-4f_{2}+6f_{3}-4f_{4}+f_{5}-\frac{1}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=-f_{0}+6f_{1}-14f_{2}+16f_{3}-9f_{4}+2f_{5}+\frac{5}{6}h^{6}f^{(6)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=-2f_{0}+11f_{1}-24f_{2}+26f_{3}-14f_{4}+3f_{5}+\frac{17}{6}h^{6}f^{(6)}(\xi)$$

6-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}-\frac{5}{2}h^{6}f^{(6)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}-\frac{3}{2}h^{6}f^{(6)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}-\frac{1}{2}h^{6}f^{(6)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}+\frac{1}{2}h^{6}f^{(6)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}+\frac{3}{2}h^{6}f^{(6)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=-f_{0}+5f_{1}-10f_{2}+10f_{3}-5f_{4}+f_{5}+\frac{5}{2}h^{6}f^{(6)}(\xi)$$

7-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{60}(-147f_{0}+360f_{1}-450f_{2}+400f_{3}-225f_{4}+72f_{5}-10f_{6})+\frac{1}{7}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{60}(-10f_{0}-77f_{1}+150f_{2}-100f_{3}+50f_{4}-15f_{5}+2f_{6})-\frac{1}{42}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{60}(2f_{0}-24f_{1}-35f_{2}+80f_{3}-30f_{4}+8f_{5}-f_{6})+\frac{1}{105}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{60}(-f_{0}+9f_{1}-45f_{2}+45f_{4}-9f_{5}+f_{6})-\frac{1}{140}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{60}(f_{0}-8f_{1}+30f_{2}-80f_{3}+35f_{4}+24f_{5}-2f_{6})+\frac{1}{105}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{60}(-2f_{0}+15f_{1}-50f_{2}+100f_{3}-150f_{4}+77f_{5}+10f_{6})-\frac{1}{42}h^{7}f^{(7)}(\xi)$$
 * $$h\,f^{(1)}(x_{6})=\frac{1}{60}(10f_{0}-72f_{1}+225f_{2}-400f_{3}+450f_{4}-360f_{5}+147f_{6})+\frac{1}{7}h^{7}f^{(7)}(\xi)$$

7-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{180}(812f_{0}-3132f_{1}+5265f_{2}-5080f_{3}+2970f_{4}-972f_{5}+137f_{6})-\frac{7}{10}h^{7}f^{(7)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{180}(137f_{0}-147f_{1}-255f_{2}+470f_{3}-285f_{4}+93f_{5}-13f_{6})+\frac{11}{180}h^{7}f^{(7)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{180}(-13f_{0}+228f_{1}-420f_{2}+200f_{3}+15f_{4}-12f_{5}+2f_{6})-\frac{1}{90}h^{7}f^{(7)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{180}(2f_{0}-27f_{1}+270f_{2}-490f_{3}+270f_{4}-27f_{5}+2f_{6})-\frac{1}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{180}(2f_{0}-12f_{1}+15f_{2}+200f_{3}-420f_{4}+228f_{5}-13f_{6})+\frac{1}{90}h^{7}f^{(7)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{180}(-13f_{0}+93f_{1}-285f_{2}+470f_{3}-255f_{4}-147f_{5}+137f_{6})-\frac{11}{180}h^{7}f^{(7)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{6})=\frac{1}{180}(137f_{0}-972f_{1}+2970f_{2}-5080f_{3}+5265f_{4}-3132f_{5}+812f_{6})+\frac{7}{10}h^{7}f^{(7)}(\xi)$$

7-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{8}(-49f_{0}+232f_{1}-461f_{2}+496f_{3}-307f_{4}+104f_{5}-15f_{6})+\frac{29}{15}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{8}(-15f_{0}+56f_{1}-83f_{2}+64f_{3}-29f_{4}+8f_{5}-f_{6})+\frac{7}{120}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{8}(-f_{0}-8f_{1}+35f_{2}-48f_{3}+29f_{4}-8f_{5}+f_{6})-\frac{1}{15}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{8}(f_{0}-8f_{1}+13f_{2}-13f_{4}+8f_{5}-f_{6})+\frac{7}{120}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{8}(-f_{0}+8f_{1}-29f_{2}+48f_{3}-35f_{4}+8f_{5}+f_{6})-\frac{1}{15}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{8}(f_{0}-8f_{1}+29f_{2}-64f_{3}+83f_{4}-56f_{5}+15f_{6})+\frac{7}{120}h^{7}f^{(7)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{6})=\frac{1}{8}(15f_{0}-104f_{1}+307f_{2}-496f_{3}+461f_{4}-232f_{5}+49f_{6})+\frac{29}{15}h^{7}f^{(7)}(\xi)$$

7-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=\frac{1}{6}(35f_{0}-186f_{1}+411f_{2}-484f_{3}+321f_{4}-114f_{5}+17f_{6})-\frac{7}{2}h^{7}f^{(7)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=\frac{1}{6}(17f_{0}-84f_{1}+171f_{2}-184f_{3}+111f_{4}-36f_{5}+5f_{6})-\frac{2}{3}h^{7}f^{(7)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=\frac{1}{6}(5f_{0}-18f_{1}+21f_{2}-4f_{3}-9f_{4}+6f_{5}-f_{6})+\frac{1}{6}h^{7}f^{(7)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=\frac{1}{6}(-f_{0}+12f_{1}-39f_{2}+56f_{3}-39f_{4}+12f_{5}-f_{6})+\frac{7}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=\frac{1}{6}(-f_{0}+6f_{1}-9f_{2}-4f_{3}+21f_{4}-18f_{5}+5f_{6})-\frac{1}{6}h^{7}f^{(7)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=\frac{1}{6}(5f_{0}-36f_{1}+111f_{2}-184f_{3}+171f_{4}-84f_{5}+17f_{6})+\frac{2}{3}h^{7}f^{(7)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{6})=\frac{1}{6}(17f_{0}-114f_{1}+321f_{2}-484f_{3}+411f_{4}-186f_{5}+35f_{6})+\frac{7}{2}h^{7}f^{(7)}(\xi)$$

7-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=\frac{1}{2}(-7f_{0}+40f_{1}-95f_{2}+120f_{3}-85f_{4}+32f_{5}-5f_{6})+\frac{25}{6}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=\frac{1}{2}(-5f_{0}+28f_{1}-65f_{2}+80f_{3}-55f_{4}+20f_{5}-3f_{6})+\frac{5}{3}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=\frac{1}{2}(-3f_{0}+16f_{1}-35f_{2}+40f_{3}-25f_{4}+8f_{5}-f_{6})+\frac{1}{6}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=\frac{1}{2}(-f_{0}+4f_{1}-5f_{2}+5f_{4}-4f_{5}+f_{6})-\frac{1}{3}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=\frac{1}{2}(f_{0}-8f_{1}+25f_{2}-40f_{3}+35f_{4}-16f_{5}+3f_{6})+\frac{1}{6}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=\frac{1}{2}(3f_{0}-20f_{1}+55f_{2}-80f_{3}+65f_{4}-28f_{5}+5f_{6})+\frac{5}{3}h^{7}f^{(7)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{6})=\frac{1}{2}(5f_{0}-32f_{1}+85f_{2}-120f_{3}+95f_{4}-40f_{5}+7f_{6})+\frac{25}{6}h^{7}f^{(7)}(\xi)$$

7-punts 6e afgeleide:
 * $$h^{6}f^{(6)}(x_{0})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}-3h^{7}f^{(7)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{1})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}-2h^{7}f^{(7)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{2})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}-h^{7}f^{(7)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{3})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}-\frac{1}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{4})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}+h^{7}f^{(7)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{5})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}+2h^{7}f^{(7)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{6})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}+3h^{7}f^{(7)}(\xi)$$

8-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{420}(-1089f_{0}+2940f_{1}-4410f_{2}+4900f_{3}-3675f_{4}+1764f_{5}-490f_{6}+60f_{7})-\frac{1}{8}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{420}(-60f_{0}-609f_{1}+1260f_{2}-1050f_{3}+700f_{4}-315f_{5}+84f_{6}-10f_{7})+\frac{1}{56}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{420}(10f_{0}-140f_{1}-329f_{2}+700f_{3}-350f_{4}+140f_{5}-35f_{6}+4f_{7})-\frac{1}{168}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{420}(-4f_{0}+42f_{1}-252f_{2}-105f_{3}+420f_{4}-126f_{5}+28f_{6}-3f_{7})+\frac{1}{280}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{420}(3f_{0}-28f_{1}+126f_{2}-420f_{3}+105f_{4}+252f_{5}-42f_{6}+4f_{7})-\frac{1}{280}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{420}(-4f_{0}+35f_{1}-140f_{2}+350f_{3}-700f_{4}+329f_{5}+140f_{6}-10f_{7})+\frac{1}{168}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{6})=\frac{1}{420}(10f_{0}-84f_{1}+315f_{2}-700f_{3}+1050f_{4}-1260f_{5}+609f_{6}+60f_{7})-\frac{1}{56}h^{8}f^{(8)}(\xi)$$
 * $$h\,f^{(1)}(x_{7})=\frac{1}{420}(-60f_{0}+490f_{1}-1764f_{2}+3675f_{3}-4900f_{4}+4410f_{5}-2940f_{6}+1089f_{7})+\frac{1}{8}h^{8}f^{(8)}(\xi)$$

8-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{180}(938f_{0}-4014f_{1}+7911f_{2}-9490f_{3}+7380f_{4}-3618f_{5}+1019f_{6}-126f_{7})+\frac{363}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{180}(126f_{0}-70f_{1}-486f_{2}+855f_{3}-670f_{4}+324f_{5}-90f_{6}+11f_{7})-\frac{29}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{180}(-11f_{0}+214f_{1}-378f_{2}+130f_{3}+85f_{4}-54f_{5}+16f_{6}-2f_{7})+\frac{47}{5040}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{180}(2f_{0}-27f_{1}+270f_{2}-490f_{3}+270f_{4}-27f_{5}+2f_{6})-\frac{1}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{180}(2f_{1}-27f_{2}+270f_{3}-490f_{4}+270f_{5}-27f_{6}+2f_{7})-\frac{1}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{180}(-2f_{0}+16f_{1}-54f_{2}+85f_{3}+130f_{4}-378f_{5}+214f_{6}-11f_{7})+\frac{47}{5040}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{6})=\frac{1}{180}(11f_{0}-90f_{1}+324f_{2}-670f_{3}+855f_{4}-486f_{5}-70f_{6}+126f_{7})-\frac{29}{560}h^{8}f^{(8)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{7})=\frac{1}{180}(-126f_{0}+1019f_{1}-3618f_{2}+7380f_{3}-9490f_{4}+7911f_{5}-4014f_{6}+938f_{7})+\frac{363}{560}h^{8}f^{(8)}(\xi)$$

8-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{120}(-967f_{0}+5104f_{1}-11787f_{2}+15560f_{3}-12725f_{4}+6432f_{5}-1849f_{6}+232f_{7})-\frac{469}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{120}(-232f_{0}+889f_{1}-1392f_{2}+1205f_{3}-680f_{4}+267f_{5}-64f_{6}+7f_{7})-\frac{1}{48}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{120}(-7f_{0}-176f_{1}+693f_{2}-1000f_{3}+715f_{4}-288f_{5}+71f_{6}-8f_{7})+\frac{3}{80}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{120}(8f_{0}-71f_{1}+48f_{2}+245f_{3}-440f_{4}+267f_{5}-64f_{6}+7f_{7})-\frac{7}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{120}(-7f_{0}+64f_{1}-267f_{2}+440f_{3}-245f_{4}-48f_{5}+71f_{6}-8f_{7})+\frac{7}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{120}(8f_{0}-71f_{1}+288f_{2}-715f_{3}+1000f_{4}-693f_{5}+176f_{6}+7f_{7})-\frac{3}{80}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{6})=\frac{1}{120}(-7f_{0}+64f_{1}-267f_{2}+680f_{3}-1205f_{4}+1392f_{5}-889f_{6}+232f_{7})+\frac{1}{48}h^{8}f^{(8)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{7})=\frac{1}{120}(-232f_{0}+1849f_{1}-6432f_{2}+12725f_{3}-15560f_{4}+11787f_{5}-5104f_{6}+967f_{7})+\frac{469}{240}h^{8}f^{(8)}(\xi)$$

8-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=\frac{1}{6}(56f_{0}-333f_{1}+852f_{2}-1219f_{3}+1056f_{4}-555f_{5}+164f_{6}-21f_{7})+\frac{967}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=\frac{1}{6}(21f_{0}-112f_{1}+255f_{2}-324f_{3}+251f_{4}-120f_{5}+33f_{6}-4f_{7})+\frac{127}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=\frac{1}{6}(4f_{0}-11f_{1}+31f_{3}-44f_{4}+27f_{5}-8f_{6}+f_{7})-\frac{11}{80}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=\frac{1}{6}(-f_{0}+12f_{1}-39f_{2}+56f_{3}-39f_{4}+12f_{5}-f_{6})+\frac{7}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=\frac{1}{6}(-f_{1}+12f_{2}-39f_{3}+56f_{4}-39f_{5}+12f_{6}-f_{7})+\frac{7}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=\frac{1}{6}(f_{0}-8f_{1}+27f_{2}-44f_{3}+31f_{4}-11f_{6}+4f_{7})-\frac{11}{80}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{6})=\frac{1}{6}(-4f_{0}+33f_{1}-120f_{2}+251f_{3}-324f_{4}+255f_{5}-112f_{6}+21f_{7})+\frac{127}{240}h^{8}f^{(8)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{7})=\frac{1}{6}(-21f_{0}+164f_{1}-555f_{2}+1056f_{3}-1219f_{4}+852f_{5}-333f_{6}+56f_{7})+\frac{967}{240}h^{8}f^{(8)}(\xi)$$

8-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=\frac{1}{6}(-46f_{0}+295f_{1}-810f_{2}+1235f_{3}-1130f_{4}+621f_{5}-190f_{6}+25f_{7})-\frac{35}{6}h^{8}f^{(8)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=\frac{1}{6}(-25f_{0}+154f_{1}-405f_{2}+590f_{3}-515f_{4}+270f_{5}-79f_{6}+10f_{7})-\frac{5}{3}h^{8}f^{(8)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=\frac{1}{6}(-10f_{0}+55f_{1}-126f_{2}+155f_{3}-110f_{4}+45f_{5}-10f_{6}+f_{7})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=\frac{1}{6}(-f_{0}-2f_{1}+27f_{2}-70f_{3}+85f_{4}-54f_{5}+17f_{6}-2f_{7})+\frac{1}{6}h^{8}f^{(8)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=\frac{1}{6}(2f_{0}-17f_{1}+54f_{2}-85f_{3}+70f_{4}-27f_{5}+2f_{6}+f_{7})-\frac{1}{6}h^{8}f^{(8)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=\frac{1}{6}(-f_{0}+10f_{1}-45f_{2}+110f_{3}-155f_{4}+126f_{5}-55f_{6}+10f_{7})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{6})=\frac{1}{6}(-10f_{0}+79f_{1}-270f_{2}+515f_{3}-590f_{4}+405f_{5}-154f_{6}+25f_{7})+\frac{5}{3}h^{8}f^{(8)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{7})=\frac{1}{6}(-25f_{0}+190f_{1}-621f_{2}+1130f_{3}-1235f_{4}+810f_{5}-295f_{6}+46f_{7})+\frac{35}{6}h^{8}f^{(8)}(\xi)$$

8-punts 6e afgeleide:
 * $$h^{6}f^{(6)}(x_{0})=4f_{0}-27f_{1}+78f_{2}-125f_{3}+120f_{4}-69f_{5}+22f_{6}-3f_{7}+\frac{23}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{1})=3f_{0}-20f_{1}+57f_{2}-90f_{3}+85f_{4}-48f_{5}+15f_{6}-2f_{7}+\frac{11}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{2})=2f_{0}-13f_{1}+36f_{2}-55f_{3}+50f_{4}-27f_{5}+8f_{6}-f_{7}+\frac{3}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{3})=f_{0}-6f_{1}+15f_{2}-20f_{3}+15f_{4}-6f_{5}+f_{6}-\frac{1}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{4})=f_{1}-6f_{2}+15f_{3}-20f_{4}+15f_{5}-6f_{6}+f_{7}-\frac{1}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{5})=-f_{0}+8f_{1}-27f_{2}+50f_{3}-55f_{4}+36f_{5}-13f_{6}+2f_{7}+\frac{3}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{6})=-2f_{0}+15f_{1}-48f_{2}+85f_{3}-90f_{4}+57f_{5}-20f_{6}+3f_{7}+\frac{11}{4}h^{8}f^{(8)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{7})=-3f_{0}+22f_{1}-69f_{2}+120f_{3}-125f_{4}+78f_{5}-27f_{6}+4f_{7}+\frac{23}{4}h^{8}f^{(8)}(\xi)$$

8-punts 7e afgeleide:
 * $$h^{7}f^{(7)}(x_{0})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}-\frac{7}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{1})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}-\frac{5}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{2})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}-\frac{3}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{3})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}-\frac{1}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{4})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}+\frac{1}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{5})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}+\frac{3}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{6})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}+\frac{5}{2}h^{8}f^{(8)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{7})=-f_{0}+7f_{1}-21f_{2}+35f_{3}-35f_{4}+21f_{5}-7f_{6}+f_{7}+\frac{7}{2}h^{8}f^{(8)}(\xi)$$

9-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{840}(-2283f_{0}+6720f_{1}-11760f_{2}+15680f_{3}-14700f_{4}+9408f_{5}-3920f_{6}+960f_{7}-105f_{8})+\frac{1}{9}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{840}(-105f_{0}-1338f_{1}+2940f_{2}-2940f_{3}+2450f_{4}-1470f_{5}+588f_{6}-140f_{7}+15f_{8})-\frac{1}{72}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{840}(15f_{0}-240f_{1}-798f_{2}+1680f_{3}-1050f_{4}+560f_{5}-210f_{6}+48f_{7}-5f_{8})+\frac{1}{252}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{840}(-5f_{0}+60f_{1}-420f_{2}-378f_{3}+1050f_{4}-420f_{5}+140f_{6}-30f_{7}+3f_{8})-\frac{1}{504}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{840}(3f_{0}-32f_{1}+168f_{2}-672f_{3}+672f_{5}-168f_{6}+32f_{7}-3f_{8})+\frac{1}{630}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{840}(-3f_{0}+30f_{1}-140f_{2}+420f_{3}-1050f_{4}+378f_{5}+420f_{6}-60f_{7}+5f_{8})-\frac{1}{504}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{6})=\frac{1}{840}(5f_{0}-48f_{1}+210f_{2}-560f_{3}+1050f_{4}-1680f_{5}+798f_{6}+240f_{7}-15f_{8})+\frac{1}{252}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{7})=\frac{1}{840}(-15f_{0}+140f_{1}-588f_{2}+1470f_{3}-2450f_{4}+2940f_{5}-2940f_{6}+1338f_{7}+105f_{8})-\frac{1}{72}h^{9}f^{(9)}(\xi)$$
 * $$h\,f^{(1)}(x_{8})=\frac{1}{840}(105f_{0}-960f_{1}+3920f_{2}-9408f_{3}+14700f_{4}-15680f_{5}+11760f_{6}-6720f_{7}+2283f_{8})+\frac{1}{9}h^{9}f^{(9)}(\xi)$$

9-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{5040}(29531f_{0}-138528f_{1}+312984f_{2}-448672f_{3}+435330f_{4}-284256f_{5}+120008f_{6}-29664f_{7}+3267f_{8})-\frac{761}{1260}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{5040}(3267f_{0}+128f_{1}-20916f_{2}+38556f_{3}-37030f_{4}+23688f_{5}-9828f_{6}+2396f_{7}-261f_{8})+\frac{223}{5040}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{5040}(-261f_{0}+5616f_{1}-9268f_{2}+1008f_{3}+5670f_{4}-4144f_{5}+1764f_{6}-432f_{7}+47f_{8})-\frac{19}{2520}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{5040}(47f_{0}-684f_{1}+7308f_{2}-13216f_{3}+6930f_{4}-252f_{5}-196f_{6}+72f_{7}-9f_{8})+\frac{1}{560}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{5040}(-9f_{0}+128f_{1}-1008f_{2}+8064f_{3}-14350f_{4}+8064f_{5}-1008f_{6}+128f_{7}-9f_{8})+\frac{1}{3150}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{5040}(-9f_{0}+72f_{1}-196f_{2}-252f_{3}+6930f_{4}-13216f_{5}+7308f_{6}-684f_{7}+47f_{8})-\frac{1}{560}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{6})=\frac{1}{5040}(47f_{0}-432f_{1}+1764f_{2}-4144f_{3}+5670f_{4}+1008f_{5}-9268f_{6}+5616f_{7}-261f_{8})+\frac{19}{2520}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{7})=\frac{1}{5040}(-261f_{0}+2396f_{1}-9828f_{2}+23688f_{3}-37030f_{4}+38556f_{5}-20916f_{6}+128f_{7}+3267f_{8})-\frac{223}{5040}h^{9}f^{(9)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{8})=\frac{1}{5040}(3267f_{0}-29664f_{1}+120008f_{2}-284256f_{3}+435330f_{4}-448672f_{5}+312984f_{6}-138528f_{7}+29531f_{8})+\frac{761}{1260}h^{9}f^{(9)}(\xi)$$

9-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{240}(-2403f_{0}+13960f_{1}-36706f_{2}+57384f_{3}-58280f_{4}+39128f_{5}-16830f_{6}+4216f_{7}-469f_{8})+\frac{29531}{15120}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{240}(-469f_{0}+1818f_{1}-2924f_{2}+2690f_{3}-1710f_{4}+814f_{5}-268f_{6}+54f_{7}-5f_{8})-\frac{1}{945}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{240}(-5f_{0}-424f_{1}+1638f_{2}-2504f_{3}+2060f_{4}-1080f_{5}+394f_{6}-88f_{7}+9f_{8})-\frac{331}{15120}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{240}(9f_{0}-86f_{1}-100f_{2}+882f_{3}-1370f_{4}+926f_{5}-324f_{6}+70f_{7}-7f_{8})+\frac{59}{3780}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{240}(-7f_{0}+72f_{1}-338f_{2}+488f_{3}-488f_{5}+338f_{6}-72f_{7}+7f_{8})-\frac{41}{3024}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{240}(7f_{0}-70f_{1}+324f_{2}-926f_{3}+1370f_{4}-882f_{5}+100f_{6}+86f_{7}-9f_{8})+\frac{59}{3780}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{6})=\frac{1}{240}(-9f_{0}+88f_{1}-394f_{2}+1080f_{3}-2060f_{4}+2504f_{5}-1638f_{6}+424f_{7}+5f_{8})-\frac{331}{15120}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{7})=\frac{1}{240}(5f_{0}-54f_{1}+268f_{2}-814f_{3}+1710f_{4}-2690f_{5}+2924f_{6}-1818f_{7}+469f_{8})-\frac{1}{945}h^{9}f^{(9)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{8})=\frac{1}{240}(469f_{0}-4216f_{1}+16830f_{2}-39128f_{3}+58280f_{4}-57384f_{5}+36706f_{6}-13960f_{7}+2403f_{8})+\frac{29531}{15120}h^{9}f^{(9)}(\xi)$$

9-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=\frac{1}{240}(3207f_{0}-21056f_{1}+61156f_{2}-102912f_{3}+109930f_{4}-76352f_{5}+33636f_{6}-8576f_{7}+967f_{8})-\frac{89}{20}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=\frac{1}{240}(967f_{0}-5496f_{1}+13756f_{2}-20072f_{3}+18930f_{4}-11912f_{5}+4876f_{6}-1176f_{7}+127f_{8})-\frac{101}{240}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=\frac{1}{240}(127f_{0}-176f_{1}-924f_{2}+3088f_{3}-4070f_{4}+2928f_{5}-1244f_{6}+304f_{7}-33f_{8})+\frac{13}{120}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=\frac{1}{240}(-33f_{0}+424f_{1}-1364f_{2}+1848f_{3}-1070f_{4}+88f_{5}+156f_{6}-56f_{7}+7f_{8})-\frac{7}{240}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=\frac{1}{240}(7f_{0}-96f_{1}+676f_{2}-1952f_{3}+2730f_{4}-1952f_{5}+676f_{6}-96f_{7}+7f_{8})-\frac{41}{7560}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=\frac{1}{240}(7f_{0}-56f_{1}+156f_{2}+88f_{3}-1070f_{4}+1848f_{5}-1364f_{6}+424f_{7}-33f_{8})+\frac{7}{240}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{6})=\frac{1}{240}(-33f_{0}+304f_{1}-1244f_{2}+2928f_{3}-4070f_{4}+3088f_{5}-924f_{6}-176f_{7}+127f_{8})-\frac{13}{120}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{7})=\frac{1}{240}(127f_{0}-1176f_{1}+4876f_{2}-11912f_{3}+18930f_{4}-20072f_{5}+13756f_{6}-5496f_{7}+967f_{8})+\frac{101}{240}h^{9}f^{(9)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{8})=\frac{1}{240}(967f_{0}-8576f_{1}+33636f_{2}-76352f_{3}+109930f_{4}-102912f_{5}+61156f_{6}-21056f_{7}+3207f_{8})+\frac{89}{20}h^{9}f^{(9)}(\xi)$$

9-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=\frac{1}{6}(-81f_{0}+575f_{1}-1790f_{2}+3195f_{3}-3580f_{4}+2581f_{5}-1170f_{6}+305f_{7}-35f_{8})+\frac{1069}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=\frac{1}{6}(-35f_{0}+234f_{1}-685f_{2}+1150f_{3}-1215f_{4}+830f_{5}-359f_{6}+90f_{7}-10f_{8})+\frac{229}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=\frac{1}{6}(-10f_{0}+55f_{1}-126f_{2}+155f_{3}-110f_{4}+45f_{5}-10f_{6}+f_{7})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=\frac{1}{6}(-10f_{1}+55f_{2}-126f_{3}+155f_{4}-110f_{5}+45f_{6}-10f_{7}+f_{8})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=\frac{1}{6}(f_{0}-9f_{1}+26f_{2}-29f_{3}+29f_{5}-26f_{6}+9f_{7}-f_{8})+\frac{13}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=\frac{1}{6}(-f_{0}+10f_{1}-45f_{2}+110f_{3}-155f_{4}+126f_{5}-55f_{6}+10f_{7})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{6})=\frac{1}{6}(-f_{1}+10f_{2}-45f_{3}+110f_{4}-155f_{5}+126f_{6}-55f_{7}+10f_{8})-\frac{11}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{7})=\frac{1}{6}(10f_{0}-90f_{1}+359f_{2}-830f_{3}+1215f_{4}-1150f_{5}+685f_{6}-234f_{7}+35f_{8})+\frac{229}{144}h^{9}f^{(9)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{8})=\frac{1}{6}(35f_{0}-305f_{1}+1170f_{2}-2581f_{3}+3580f_{4}-3195f_{5}+1790f_{6}-575f_{7}+81f_{8})+\frac{1069}{144}h^{9}f^{(9)}(\xi)$$

9-punts 6e afgeleide:
 * $$h^{6}f^{(6)}(x_{0})=\frac{1}{4}(39f_{0}-292f_{1}+956f_{2}-1788f_{3}+2090f_{4}-1564f_{5}+732f_{6}-196f_{7}+23f_{8})-9h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{1})=\frac{1}{4}(23f_{0}-168f_{1}+536f_{2}-976f_{3}+1110f_{4}-808f_{5}+368f_{6}-96f_{7}+11f_{8})-\frac{13}{4}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{2})=\frac{1}{4}(11f_{0}-76f_{1}+228f_{2}-388f_{3}+410f_{4}-276f_{5}+116f_{6}-28f_{7}+3f_{8})-\frac{1}{2}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{3})=\frac{1}{4}(3f_{0}-16f_{1}+32f_{2}-24f_{3}-10f_{4}+32f_{5}-24f_{6}+8f_{7}-f_{8})+\frac{1}{4}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{4})=\frac{1}{4}(-f_{0}+12f_{1}-52f_{2}+116f_{3}-150f_{4}+116f_{5}-52f_{6}+12f_{7}-f_{8})+\frac{13}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{5})=\frac{1}{4}(-f_{0}+8f_{1}-24f_{2}+32f_{3}-10f_{4}-24f_{5}+32f_{6}-16f_{7}+3f_{8})-\frac{1}{4}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{6})=\frac{1}{4}(3f_{0}-28f_{1}+116f_{2}-276f_{3}+410f_{4}-388f_{5}+228f_{6}-76f_{7}+11f_{8})+\frac{1}{2}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{7})=\frac{1}{4}(11f_{0}-96f_{1}+368f_{2}-808f_{3}+1110f_{4}-976f_{5}+536f_{6}-168f_{7}+23f_{8})+\frac{13}{4}h^{9}f^{(9)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{8})=\frac{1}{4}(23f_{0}-196f_{1}+732f_{2}-1564f_{3}+2090f_{4}-1788f_{5}+956f_{6}-292f_{7}+39f_{8})+9h^{9}f^{(9)}(\xi)$$

9-punts 7e afgeleide:
 * $$h^{7}f^{(7)}(x_{0})=\frac{1}{2}(-9f_{0}+70f_{1}-238f_{2}+462f_{3}-560f_{4}+434f_{5}-210f_{6}+58f_{7}-7f_{8})+\frac{91}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{1})=\frac{1}{2}(-7f_{0}+54f_{1}-182f_{2}+350f_{3}-420f_{4}+322f_{5}-154f_{6}+42f_{7}-5f_{8})+\frac{49}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{2})=\frac{1}{2}(-5f_{0}+38f_{1}-126f_{2}+238f_{3}-280f_{4}+210f_{5}-98f_{6}+26f_{7}-3f_{8})+\frac{19}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{3})=\frac{1}{2}(-3f_{0}+22f_{1}-70f_{2}+126f_{3}-140f_{4}+98f_{5}-42f_{6}+10f_{7}-f_{8})+\frac{1}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{4})=\frac{1}{2}(-f_{0}+6f_{1}-14f_{2}+14f_{3}-14f_{5}+14f_{6}-6f_{7}+f_{8})-\frac{5}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{5})=\frac{1}{2}(f_{0}-10f_{1}+42f_{2}-98f_{3}+140f_{4}-126f_{5}+70f_{6}-22f_{7}+3f_{8})+\frac{1}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{6})=\frac{1}{2}(3f_{0}-26f_{1}+98f_{2}-210f_{3}+280f_{4}-238f_{5}+126f_{6}-38f_{7}+5f_{8})+\frac{19}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{7})=\frac{1}{2}(5f_{0}-42f_{1}+154f_{2}-322f_{3}+420f_{4}-350f_{5}+182f_{6}-54f_{7}+7f_{8})+\frac{49}{12}h^{9}f^{(9)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{8})=\frac{1}{2}(7f_{0}-58f_{1}+210f_{2}-434f_{3}+560f_{4}-462f_{5}+238f_{6}-70f_{7}+9f_{8})+\frac{91}{12}h^{9}f^{(9)}(\xi)$$

9-punts 8e afgeleide:
 * $$h^{8}f^{(8)}(x_{0})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-4h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{1})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-3h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{2})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-2h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{3})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{4})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-\frac{1}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{5})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}+h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{6})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}+2h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{7})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}+3h^{9}f^{(9)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{8})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}+4h^{9}f^{(9)}(\xi)$$

10-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{2520}(-7129f_{0}+22680f_{1}-45360f_{2}+70560f_{3}-79380f_{4}+63504f_{5}-35280f_{6}+12960f_{7}-2835f_{8}+280f_{9})-\frac{1}{10}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{2520}(-280f_{0}-4329f_{1}+10080f_{2}-11760f_{3}+11760f_{4}-8820f_{5}+4704f_{6}-1680f_{7}+360f_{8}-35f_{9})+\frac{1}{90}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{2520}(35f_{0}-630f_{1}-2754f_{2}+5880f_{3}-4410f_{4}+2940f_{5}-1470f_{6}+504f_{7}-105f_{8}+10f_{9})-\frac{1}{360}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{2520}(-10f_{0}+135f_{1}-1080f_{2}-1554f_{3}+3780f_{4}-1890f_{5}+840f_{6}-270f_{7}+54f_{8}-5f_{9})+\frac{1}{840}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{2520}(5f_{0}-60f_{1}+360f_{2}-1680f_{3}-504f_{4}+2520f_{5}-840f_{6}+240f_{7}-45f_{8}+4f_{9})-\frac{1}{1260}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{2520}(-4f_{0}+45f_{1}-240f_{2}+840f_{3}-2520f_{4}+504f_{5}+1680f_{6}-360f_{7}+60f_{8}-5f_{9})+\frac{1}{1260}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{6})=\frac{1}{2520}(5f_{0}-54f_{1}+270f_{2}-840f_{3}+1890f_{4}-3780f_{5}+1554f_{6}+1080f_{7}-135f_{8}+10f_{9})-\frac{1}{840}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{7})=\frac{1}{2520}(-10f_{0}+105f_{1}-504f_{2}+1470f_{3}-2940f_{4}+4410f_{5}-5880f_{6}+2754f_{7}+630f_{8}-35f_{9})+\frac{1}{360}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{8})=\frac{1}{2520}(35f_{0}-360f_{1}+1680f_{2}-4704f_{3}+8820f_{4}-11760f_{5}+11760f_{6}-10080f_{7}+4329f_{8}+280f_{9})-\frac{1}{90}h^{10}f^{(10)}(\xi)$$
 * $$h\,f^{(1)}(x_{9})=\frac{1}{2520}(-280f_{0}+2835f_{1}-12960f_{2}+35280f_{3}-63504f_{4}+79380f_{5}-70560f_{6}+45360f_{7}-22680f_{8}+7129f_{9})+\frac{1}{10}h^{10}f^{(10)}(\xi)$$

10-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{5040}(32575f_{0}-165924f_{1}+422568f_{2}-704368f_{3}+818874f_{4}-667800f_{5}+375704f_{6}-139248f_{7}+30663f_{8}-3044f_{9})+\frac{7129}{12600}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{5040}(3044f_{0}+2135f_{1}-28944f_{2}+57288f_{3}-65128f_{4}+51786f_{5}-28560f_{6}+10424f_{7}-2268f_{8}+223f_{9})-\frac{481}{12600}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{5040}(-223f_{0}+5274f_{1}-7900f_{2}-2184f_{3}+10458f_{4}-8932f_{5}+4956f_{6}-1800f_{7}+389f_{8}-38f_{9})+\frac{17}{2800}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{5040}(38f_{0}-603f_{1}+6984f_{2}-12460f_{3}+5796f_{4}+882f_{5}-952f_{6}+396f_{7}-90f_{8}+9f_{9})-\frac{37}{25200}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{5040}(-9f_{0}+128f_{1}-1008f_{2}+8064f_{3}-14350f_{4}+8064f_{5}-1008f_{6}+128f_{7}-9f_{8})+\frac{1}{3150}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{5040}(-9f_{1}+128f_{2}-1008f_{3}+8064f_{4}-14350f_{5}+8064f_{6}-1008f_{7}+128f_{8}-9f_{9})+\frac{1}{3150}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{6})=\frac{1}{5040}(9f_{0}-90f_{1}+396f_{2}-952f_{3}+882f_{4}+5796f_{5}-12460f_{6}+6984f_{7}-603f_{8}+38f_{9})-\frac{37}{25200}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{7})=\frac{1}{5040}(-38f_{0}+389f_{1}-1800f_{2}+4956f_{3}-8932f_{4}+10458f_{5}-2184f_{6}-7900f_{7}+5274f_{8}-223f_{9})+\frac{17}{2800}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{8})=\frac{1}{5040}(223f_{0}-2268f_{1}+10424f_{2}-28560f_{3}+51786f_{4}-65128f_{5}+57288f_{6}-28944f_{7}+2135f_{8}+3044f_{9})-\frac{481}{12600}h^{10}f^{(10)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{9})=\frac{1}{5040}(-3044f_{0}+30663f_{1}-139248f_{2}+375704f_{3}-667800f_{4}+818874f_{5}-704368f_{6}+422568f_{7}-165924f_{8}+32575f_{9})+\frac{7129}{12600}h^{10}f^{(10)}(\xi)$$

10-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{15120}(-180920f_{0}+1145259f_{1}-3375594f_{2}+6095796f_{3}-7392546f_{4}+6185970f_{5}-3540894f_{6}+1328724f_{7}-295326f_{8}+29531f_{9})-\frac{1303}{672}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{15120}(-29531f_{0}+114390f_{1}-183636f_{2}+168126f_{3}-105714f_{4}+49266f_{5}-15540f_{6}+2826f_{7}-171f_{8}-16f_{9})+\frac{61}{4320}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{15120}(16f_{0}-29691f_{1}+115110f_{2}-185556f_{3}+171486f_{4}-109746f_{5}+52626f_{6}-17460f_{7}+3546f_{8}-331f_{9})+\frac{79}{6048}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{15120}(331f_{0}-3294f_{1}-14796f_{2}+75390f_{3}-116046f_{4}+88074f_{5}-40236f_{6}+12906f_{7}-2565f_{8}+236f_{9})-\frac{89}{10080}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{15120}(-236f_{0}+2691f_{1}-13914f_{2}+13524f_{3}+25830f_{4}-56574f_{5}+38514f_{6}-11916f_{7}+2286f_{8}-205f_{9})+\frac{41}{6048}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{15120}(205f_{0}-2286f_{1}+11916f_{2}-38514f_{3}+56574f_{4}-25830f_{5}-13524f_{6}+13914f_{7}-2691f_{8}+236f_{9})-\frac{41}{6048}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{6})=\frac{1}{15120}(-236f_{0}+2565f_{1}-12906f_{2}+40236f_{3}-88074f_{4}+116046f_{5}-75390f_{6}+14796f_{7}+3294f_{8}-331f_{9})+\frac{89}{10080}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{7})=\frac{1}{15120}(331f_{0}-3546f_{1}+17460f_{2}-52626f_{3}+109746f_{4}-171486f_{5}+185556f_{6}-115110f_{7}+29691f_{8}-16f_{9})-\frac{79}{6048}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{8})=\frac{1}{15120}(16f_{0}+171f_{1}-2826f_{2}+15540f_{3}-49266f_{4}+105714f_{5}-168126f_{6}+183636f_{7}-114390f_{8}+29531f_{9})-\frac{61}{4320}h^{10}f^{(10)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{9})=\frac{1}{15120}(-29531f_{0}+295326f_{1}-1328724f_{2}+3540894f_{3}-6185970f_{4}+7392546f_{5}-6095796f_{6}+3375594f_{7}-1145259f_{8}+180920f_{9})+\frac{1303}{672}h^{10}f^{(10)}(\xi)$$

10-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=\frac{1}{240}(4275f_{0}-30668f_{1}+99604f_{2}-192624f_{3}+244498f_{4}-210920f_{5}+123348f_{6}-47024f_{7}+10579f_{8}-1068f_{9})+\frac{4523}{945}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=\frac{1}{240}(1068f_{0}-6405f_{1}+17392f_{2}-28556f_{3}+31656f_{4}-24638f_{5}+13360f_{6}-4812f_{7}+1036f_{8}-101f_{9})+\frac{1271}{3780}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=\frac{1}{240}(101f_{0}+58f_{1}-1860f_{2}+5272f_{3}-7346f_{4}+6204f_{5}-3428f_{6}+1240f_{7}-267f_{8}+26f_{9})-\frac{1279}{15120}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=\frac{1}{240}(-26f_{0}+361f_{1}-1112f_{2}+1260f_{3}-188f_{4}-794f_{5}+744f_{6}-308f_{7}+70f_{8}-7f_{9})+\frac{359}{15120}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=\frac{1}{240}(7f_{0}-96f_{1}+676f_{2}-1952f_{3}+2730f_{4}-1952f_{5}+676f_{6}-96f_{7}+7f_{8})-\frac{41}{7560}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=\frac{1}{240}(7f_{1}-96f_{2}+676f_{3}-1952f_{4}+2730f_{5}-1952f_{6}+676f_{7}-96f_{8}+7f_{9})-\frac{41}{7560}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{6})=\frac{1}{240}(-7f_{0}+70f_{1}-308f_{2}+744f_{3}-794f_{4}-188f_{5}+1260f_{6}-1112f_{7}+361f_{8}-26f_{9})+\frac{359}{15120}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{7})=\frac{1}{240}(26f_{0}-267f_{1}+1240f_{2}-3428f_{3}+6204f_{4}-7346f_{5}+5272f_{6}-1860f_{7}+58f_{8}+101f_{9})-\frac{1279}{15120}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{8})=\frac{1}{240}(-101f_{0}+1036f_{1}-4812f_{2}+13360f_{3}-24638f_{4}+31656f_{5}-28556f_{6}+17392f_{7}-6405f_{8}+1068f_{9})+\frac{1271}{3780}h^{10}f^{(10)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{9})=\frac{1}{240}(-1068f_{0}+10579f_{1}-47024f_{2}+123348f_{3}-210920f_{4}+244498f_{5}-192624f_{6}+99604f_{7}-30668f_{8}+4275f_{9})+\frac{4523}{945}h^{10}f^{(10)}(\xi)$$

10-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=\frac{1}{144}(-3013f_{0}+23421f_{1}-81444f_{2}+166476f_{3}-220614f_{4}+196638f_{5}-117876f_{6}+45804f_{7}-10461f_{8}+1069f_{9})-\frac{285}{32}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=\frac{1}{144}(-1069f_{0}+7677f_{1}-24684f_{2}+46836f_{3}-58014f_{4}+48774f_{5}-27852f_{6}+10404f_{7}-2301f_{8}+229f_{9})-\frac{427}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=\frac{1}{144}(-229f_{0}+1221f_{1}-2628f_{2}+2796f_{3}-1254f_{4}-306f_{5}+684f_{6}-372f_{7}+99f_{8}-11f_{9})+\frac{31}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=\frac{1}{144}(11f_{0}-339f_{1}+1716f_{2}-3948f_{3}+5106f_{4}-4026f_{5}+2004f_{6}-636f_{7}+123f_{8}-11f_{9})+\frac{1}{32}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=\frac{1}{144}(11f_{0}-99f_{1}+156f_{2}+396f_{3}-1638f_{4}+2334f_{5}-1716f_{6}+684f_{7}-141f_{8}+13f_{9})-\frac{13}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=\frac{1}{144}(-13f_{0}+141f_{1}-684f_{2}+1716f_{3}-2334f_{4}+1638f_{5}-396f_{6}-156f_{7}+99f_{8}-11f_{9})+\frac{13}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{6})=\frac{1}{144}(11f_{0}-123f_{1}+636f_{2}-2004f_{3}+4026f_{4}-5106f_{5}+3948f_{6}-1716f_{7}+339f_{8}-11f_{9})-\frac{1}{32}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{7})=\frac{1}{144}(11f_{0}-99f_{1}+372f_{2}-684f_{3}+306f_{4}+1254f_{5}-2796f_{6}+2628f_{7}-1221f_{8}+229f_{9})-\frac{31}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{8})=\frac{1}{144}(-229f_{0}+2301f_{1}-10404f_{2}+27852f_{3}-48774f_{4}+58014f_{5}-46836f_{6}+24684f_{7}-7677f_{8}+1069f_{9})+\frac{427}{288}h^{10}f^{(10)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{9})=\frac{1}{144}(-1069f_{0}+10461f_{1}-45804f_{2}+117876f_{3}-196638f_{4}+220614f_{5}-166476f_{6}+81444f_{7}-23421f_{8}+3013f_{9})+\frac{285}{32}h^{10}f^{(10)}(\xi)$$

10-punts 6e afgeleide:
 * $$h^{6}f^{(6)}(x_{0})=\frac{1}{4}(75f_{0}-616f_{1}+2252f_{2}-4812f_{3}+6626f_{4}-6100f_{5}+3756f_{6}-1492f_{7}+347f_{8}-36f_{9})+\frac{3013}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{1})=\frac{1}{4}(36f_{0}-285f_{1}+1004f_{2}-2068f_{3}+2748f_{4}-2446f_{5}+1460f_{6}-564f_{7}+128f_{8}-13f_{9})+\frac{853}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{2})=\frac{1}{4}(13f_{0}-94f_{1}+300f_{2}-556f_{3}+662f_{4}-528f_{5}+284f_{6}-100f_{7}+21f_{8}-2f_{9})+\frac{73}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{3})=\frac{1}{4}(2f_{0}-7f_{1}-4f_{2}+60f_{3}-136f_{4}+158f_{5}-108f_{6}+44f_{7}-10f_{8}+f_{9})-\frac{47}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{4})=\frac{1}{4}(-f_{0}+12f_{1}-52f_{2}+116f_{3}-150f_{4}+116f_{5}-52f_{6}+12f_{7}-f_{8})+\frac{13}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{5})=\frac{1}{4}(-f_{1}+12f_{2}-52f_{3}+116f_{4}-150f_{5}+116f_{6}-52f_{7}+12f_{8}-f_{9})+\frac{13}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{6})=\frac{1}{4}(f_{0}-10f_{1}+44f_{2}-108f_{3}+158f_{4}-136f_{5}+60f_{6}-4f_{7}-7f_{8}+2f_{9})-\frac{47}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{7})=\frac{1}{4}(-2f_{0}+21f_{1}-100f_{2}+284f_{3}-528f_{4}+662f_{5}-556f_{6}+300f_{7}-94f_{8}+13f_{9})+\frac{73}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{8})=\frac{1}{4}(-13f_{0}+128f_{1}-564f_{2}+1460f_{3}-2446f_{4}+2748f_{5}-2068f_{6}+1004f_{7}-285f_{8}+36f_{9})+\frac{853}{240}h^{10}f^{(10)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{9})=\frac{1}{4}(-36f_{0}+347f_{1}-1492f_{2}+3756f_{3}-6100f_{4}+6626f_{5}-4812f_{6}+2252f_{7}-616f_{8}+75f_{9})+\frac{3013}{240}h^{10}f^{(10)}(\xi)$$

10-punts 7e afgeleide:
 * $$h^{7}f^{(7)}(x_{0})=\frac{1}{12}(-145f_{0}+1239f_{1}-4704f_{2}+10416f_{3}-14826f_{4}+14070f_{5}-8904f_{6}+3624f_{7}-861f_{8}+91f_{9})-\frac{105}{8}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{1})=\frac{1}{12}(-91f_{0}+765f_{1}-2856f_{2}+6216f_{3}-8694f_{4}+8106f_{5}-5040f_{6}+2016f_{7}-471f_{8}+49f_{9})-\frac{133}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{2})=\frac{1}{12}(-49f_{0}+399f_{1}-1440f_{2}+3024f_{3}-4074f_{4}+3654f_{5}-2184f_{6}+840f_{7}-189f_{8}+19f_{9})-\frac{35}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{3})=\frac{1}{12}(-19f_{0}+141f_{1}-456f_{2}+840f_{3}-966f_{4}+714f_{5}-336f_{6}+96f_{7}-15f_{8}+f_{9})+\frac{1}{8}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{4})=\frac{1}{12}(-f_{0}-9f_{1}+96f_{2}-336f_{3}+630f_{4}-714f_{5}+504f_{6}-216f_{7}+51f_{8}-5f_{9})+\frac{5}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{5})=\frac{1}{12}(5f_{0}-51f_{1}+216f_{2}-504f_{3}+714f_{4}-630f_{5}+336f_{6}-96f_{7}+9f_{8}+f_{9})-\frac{5}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{6})=\frac{1}{12}(-f_{0}+15f_{1}-96f_{2}+336f_{3}-714f_{4}+966f_{5}-840f_{6}+456f_{7}-141f_{8}+19f_{9})-\frac{1}{8}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{7})=\frac{1}{12}(-19f_{0}+189f_{1}-840f_{2}+2184f_{3}-3654f_{4}+4074f_{5}-3024f_{6}+1440f_{7}-399f_{8}+49f_{9})+\frac{35}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{8})=\frac{1}{12}(-49f_{0}+471f_{1}-2016f_{2}+5040f_{3}-8106f_{4}+8694f_{5}-6216f_{6}+2856f_{7}-765f_{8}+91f_{9})+\frac{133}{24}h^{10}f^{(10)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{9})=\frac{1}{12}(-91f_{0}+861f_{1}-3624f_{2}+8904f_{3}-14070f_{4}+14826f_{5}-10416f_{6}+4704f_{7}-1239f_{8}+145f_{9})+\frac{105}{8}h^{10}f^{(10)}(\xi)$$

10-punts 8e afgeleide:
 * $$h^{8}f^{(8)}(x_{0})=5f_{0}-44f_{1}+172f_{2}-392f_{3}+574f_{4}-560f_{5}+364f_{6}-152f_{7}+37f_{8}-4f_{9}+\frac{29}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{1})=4f_{0}-35f_{1}+136f_{2}-308f_{3}+448f_{4}-434f_{5}+280f_{6}-116f_{7}+28f_{8}-3f_{9}+\frac{17}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{2})=3f_{0}-26f_{1}+100f_{2}-224f_{3}+322f_{4}-308f_{5}+196f_{6}-80f_{7}+19f_{8}-2f_{9}+\frac{8}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{3})=2f_{0}-17f_{1}+64f_{2}-140f_{3}+196f_{4}-182f_{5}+112f_{6}-44f_{7}+10f_{8}-f_{9}+\frac{2}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{4})=f_{0}-8f_{1}+28f_{2}-56f_{3}+70f_{4}-56f_{5}+28f_{6}-8f_{7}+f_{8}-\frac{1}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{5})=f_{1}-8f_{2}+28f_{3}-56f_{4}+70f_{5}-56f_{6}+28f_{7}-8f_{8}+f_{9}-\frac{1}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{6})=-f_{0}+10f_{1}-44f_{2}+112f_{3}-182f_{4}+196f_{5}-140f_{6}+64f_{7}-17f_{8}+2f_{9}+\frac{2}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{7})=-2f_{0}+19f_{1}-80f_{2}+196f_{3}-308f_{4}+322f_{5}-224f_{6}+100f_{7}-26f_{8}+3f_{9}+\frac{8}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{8})=-3f_{0}+28f_{1}-116f_{2}+280f_{3}-434f_{4}+448f_{5}-308f_{6}+136f_{7}-35f_{8}+4f_{9}+\frac{17}{3}h^{10}f^{(10)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{9})=-4f_{0}+37f_{1}-152f_{2}+364f_{3}-560f_{4}+574f_{5}-392f_{6}+172f_{7}-44f_{8}+5f_{9}+\frac{29}{3}h^{10}f^{(10)}(\xi)$$

10-punts 9e afgeleide:
 * $$h^{9}f^{(9)}(x_{0})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}-\frac{9}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{1})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}-\frac{7}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{2})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}-\frac{5}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{3})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}-\frac{3}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{4})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}-\frac{1}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{5})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}+\frac{1}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{6})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}+\frac{3}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{7})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}+\frac{5}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{8})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}+\frac{7}{2}h^{10}f^{(10)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{9})=-f_{0}+9f_{1}-36f_{2}+84f_{3}-126f_{4}+126f_{5}-84f_{6}+36f_{7}-9f_{8}+f_{9}+\frac{9}{2}h^{10}f^{(10)}(\xi)$$

11-punts 1e afgeleide:
 * $$h\,f^{(1)}(x_{0})=\frac{1}{2520}(-7381f_{0}+25200f_{1}-56700f_{2}+100800f_{3}-132300f_{4}+127008f_{5}-88200f_{6}+43200f_{7}-14175f_{8}+2800f_{9}-252f_{10})+\frac{1}{11}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{1})=\frac{1}{2520}(-252f_{0}-4609f_{1}+11340f_{2}-15120f_{3}+17640f_{4}-15876f_{5}+10584f_{6}-5040f_{7}+1620f_{8}-315f_{9}+28f_{10})-\frac{1}{110}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{2})=\frac{1}{2520}(28f_{0}-560f_{1}-3069f_{2}+6720f_{3}-5880f_{4}+4704f_{5}-2940f_{6}+1344f_{7}-420f_{8}+80f_{9}-7f_{10})+\frac{1}{495}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{3})=\frac{1}{2520}(-7f_{0}+105f_{1}-945f_{2}-1914f_{3}+4410f_{4}-2646f_{5}+1470f_{6}-630f_{7}+189f_{8}-35f_{9}+3f_{10})-\frac{1}{1320}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{4})=\frac{1}{2520}(3f_{0}-40f_{1}+270f_{2}-1440f_{3}-924f_{4}+3024f_{5}-1260f_{6}+480f_{7}-135f_{8}+24f_{9}-2f_{10})+\frac{1}{2310}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{5})=\frac{1}{2520}(-2f_{0}+25f_{1}-150f_{2}+600f_{3}-2100f_{4}+2100f_{6}-600f_{7}+150f_{8}-25f_{9}+2f_{10})-\frac{1}{2772}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{6})=\frac{1}{2520}(2f_{0}-24f_{1}+135f_{2}-480f_{3}+1260f_{4}-3024f_{5}+924f_{6}+1440f_{7}-270f_{8}+40f_{9}-3f_{10})+\frac{1}{2310}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{7})=\frac{1}{2520}(-3f_{0}+35f_{1}-189f_{2}+630f_{3}-1470f_{4}+2646f_{5}-4410f_{6}+1914f_{7}+945f_{8}-105f_{9}+7f_{10})-\frac{1}{1320}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{8})=\frac{1}{2520}(7f_{0}-80f_{1}+420f_{2}-1344f_{3}+2940f_{4}-4704f_{5}+5880f_{6}-6720f_{7}+3069f_{8}+560f_{9}-28f_{10})+\frac{1}{495}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{9})=\frac{1}{2520}(-28f_{0}+315f_{1}-1620f_{2}+5040f_{3}-10584f_{4}+15876f_{5}-17640f_{6}+15120f_{7}-11340f_{8}+4609f_{9}+252f_{10})-\frac{1}{110}h^{11}f^{(11)}(\xi)$$
 * $$h\,f^{(1)}(x_{10})=\frac{1}{2520}(252f_{0}-2800f_{1}+14175f_{2}-43200f_{3}+88200f_{4}-127008f_{5}+132300f_{6}-100800f_{7}+56700f_{8}-25200f_{9}+7381f_{10})+\frac{1}{11}h^{11}f^{(11)}(\xi)$$

11-punts 2e afgeleide:
 * $$h^{2}f^{(2)}(x_{0})=\frac{1}{25200}(177133f_{0}-972200f_{1}+2754450f_{2}-5232800f_{3}+7088550f_{4}-6932016f_{5}+4872700f_{6}-2407200f_{7}+794925f_{8}-157800f_{9}+14258f_{10})-\frac{671}{1260}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{1})=\frac{1}{25200}(14258f_{0}+20295f_{1}-188010f_{2}+401880f_{3}-527660f_{4}+501354f_{5}-344820f_{6}+167560f_{7}-54630f_{8}+10735f_{9}-962f_{10})+\frac{419}{12600}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{2})=\frac{1}{25200}(-962f_{0}+24840f_{1}-32615f_{2}-29280f_{3}+84420f_{4}-83216f_{5}+56910f_{6}-27360f_{7}+8830f_{8}-1720f_{9}+153f_{10})-\frac{31}{6300}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{3})=\frac{1}{25200}(153f_{0}-2645f_{1}+33255f_{2}-57860f_{3}+21210f_{4}+13734f_{5}-12530f_{6}+6420f_{7}-2115f_{8}+415f_{9}-37f_{10})+\frac{29}{25200}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{4})=\frac{1}{25200}(-37f_{0}+560f_{1}-4680f_{2}+39360f_{3}-70070f_{4}+38304f_{5}-3360f_{6}-320f_{7}+315f_{8}-80f_{9}+8f_{10})-\frac{1}{3150}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{5})=\frac{1}{25200}(8f_{0}-125f_{1}+1000f_{2}-6000f_{3}+42000f_{4}-73766f_{5}+42000f_{6}-6000f_{7}+1000f_{8}-125f_{9}+8f_{10})-\frac{1}{16632}h^{12}f^{(12)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{6})=\frac{1}{25200}(8f_{0}-80f_{1}+315f_{2}-320f_{3}-3360f_{4}+38304f_{5}-70070f_{6}+39360f_{7}-4680f_{8}+560f_{9}-37f_{10})+\frac{1}{3150}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{7})=\frac{1}{25200}(-37f_{0}+415f_{1}-2115f_{2}+6420f_{3}-12530f_{4}+13734f_{5}+21210f_{6}-57860f_{7}+33255f_{8}-2645f_{9}+153f_{10})-\frac{29}{25200}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{8})=\frac{1}{25200}(153f_{0}-1720f_{1}+8830f_{2}-27360f_{3}+56910f_{4}-83216f_{5}+84420f_{6}-29280f_{7}-32615f_{8}+24840f_{9}-962f_{10})+\frac{31}{6300}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{9})=\frac{1}{25200}(-962f_{0}+10735f_{1}-54630f_{2}+167560f_{3}-344820f_{4}+501354f_{5}-527660f_{6}+401880f_{7}-188010f_{8}+20295f_{9}+14258f_{10})-\frac{419}{12600}h^{11}f^{(11)}(\xi)$$
 * $$h^{2}f^{(2)}(x_{10})=\frac{1}{25200}(14258f_{0}-157800f_{1}+794925f_{2}-2407200f_{3}+4872700f_{4}-6932016f_{5}+7088550f_{6}-5232800f_{7}+2754450f_{8}-972200f_{9}+177133f_{10})+\frac{671}{1260}h^{11}f^{(11)}(\xi)$$

11-punts 3e afgeleide:
 * $$h^{3}f^{(3)}(x_{0})=\frac{1}{30240}(-420475f_{0}+2876868f_{1}-9389763f_{2}+19227792f_{3}-27098442f_{4}+27147960f_{5}-19395138f_{6}+9693648f_{7}-3229227f_{8}+645412f_{9}-58635f_{10})+\frac{16103}{8400}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{1})=\frac{1}{30240}(-58635f_{0}+224510f_{1}-348057f_{2}+285012f_{3}-121758f_{4}-9072f_{5}+58590f_{6}-45588f_{7}+18873f_{8}-4302f_{9}+427f_{10})-\frac{123}{5600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{2})=\frac{1}{30240}(427f_{0}-63332f_{1}+247995f_{2}-418512f_{3}+425922f_{4}-319032f_{5}+188202f_{6}-82320f_{7}+24867f_{8}-4612f_{9}+395f_{10})-\frac{593}{75600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{3})=\frac{1}{30240}(395f_{0}-3918f_{1}-41607f_{2}+182820f_{3}-288162f_{4}+243432f_{5}-136542f_{6}+57852f_{7}-17145f_{8}+3142f_{9}-267f_{10})+\frac{263}{50400}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{4})=\frac{1}{30240}(-267f_{0}+3332f_{1}-18603f_{2}+2448f_{3}+94710f_{4}-164808f_{5}+120078f_{6}-48432f_{7}+13797f_{8}-2460f_{9}+205f_{10})-\frac{13}{3600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{5})=\frac{1}{30240}(205f_{0}-2522f_{1}+14607f_{2}-52428f_{3}+70098f_{4}-70098f_{6}+52428f_{7}-14607f_{8}+2522f_{9}-205f_{10})+\frac{479}{151200}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{6})=\frac{1}{30240}(-205f_{0}+2460f_{1}-13797f_{2}+48432f_{3}-120078f_{4}+164808f_{5}-94710f_{6}-2448f_{7}+18603f_{8}-3332f_{9}+267f_{10})-\frac{13}{3600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{7})=\frac{1}{30240}(267f_{0}-3142f_{1}+17145f_{2}-57852f_{3}+136542f_{4}-243432f_{5}+288162f_{6}-182820f_{7}+41607f_{8}+3918f_{9}-395f_{10})+\frac{263}{50400}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{8})=\frac{1}{30240}(-395f_{0}+4612f_{1}-24867f_{2}+82320f_{3}-188202f_{4}+319032f_{5}-425922f_{6}+418512f_{7}-247995f_{8}+63332f_{9}-427f_{10})-\frac{593}{75600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{9})=\frac{1}{30240}(-427f_{0}+4302f_{1}-18873f_{2}+45588f_{3}-58590f_{4}+9072f_{5}+121758f_{6}-285012f_{7}+348057f_{8}-224510f_{9}+58635f_{10})-\frac{123}{5600}h^{11}f^{(11)}(\xi)$$
 * $$h^{3}f^{(3)}(x_{10})=\frac{1}{30240}(58635f_{0}-645412f_{1}+3229227f_{2}-9693648f_{3}+19395138f_{4}-27147960f_{5}+27098442f_{6}-19227792f_{7}+9389763f_{8}-2876868f_{9}+420475f_{10})+\frac{16103}{8400}h^{11}f^{(11)}(\xi)$$

11-punts 4e afgeleide:
 * $$h^{4}f^{(4)}(x_{0})=\frac{1}{15120}(341693f_{0}-2655764f_{1}+9531612f_{2}-20819472f_{3}+30600654f_{4}-31524696f_{5}+22968204f_{6}-11646672f_{7}+3923037f_{8}-790964f_{9}+72368f_{10})-\frac{7645}{1512}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{1})=\frac{1}{15120}(72368f_{0}-454355f_{1}+1324476f_{2}-2409108f_{3}+3061968f_{4}-2833362f_{5}+1909320f_{6}-913236f_{7}+294048f_{8}-57203f_{9}+5084f_{10})-\frac{2041}{7560}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{2})=\frac{1}{15120}(5084f_{0}+16444f_{1}-174735f_{2}+485616f_{3}-731388f_{4}+713160f_{5}-484554f_{6}+231600f_{7}-74376f_{8}+14428f_{9}-1279f_{10})+\frac{167}{2520}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{3})=\frac{1}{15120}(-1279f_{0}+19153f_{1}-53901f_{2}+36300f_{3}+63546f_{4}-140490f_{5}+122262f_{6}-62484f_{7}+20565f_{8}-4031f_{9}+359f_{10})-\frac{277}{15120}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{4})=\frac{1}{15120}(359f_{0}-5228f_{1}+38898f_{2}-113136f_{3}+154770f_{4}-102312f_{5}+25368f_{6}+3792f_{7}-3249f_{8}+820f_{9}-82f_{10})+\frac{41}{7560}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{5})=\frac{1}{15120}(-82f_{0}+1261f_{1}-9738f_{2}+52428f_{3}-140196f_{4}+192654f_{5}-140196f_{6}+52428f_{7}-9738f_{8}+1261f_{9}-82f_{10})+\frac{479}{453600}h^{12}f^{(12)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{6})=\frac{1}{15120}(-82f_{0}+820f_{1}-3249f_{2}+3792f_{3}+25368f_{4}-102312f_{5}+154770f_{6}-113136f_{7}+38898f_{8}-5228f_{9}+359f_{10})-\frac{41}{7560}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{7})=\frac{1}{15120}(359f_{0}-4031f_{1}+20565f_{2}-62484f_{3}+122262f_{4}-140490f_{5}+63546f_{6}+36300f_{7}-53901f_{8}+19153f_{9}-1279f_{10})+\frac{277}{15120}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{8})=\frac{1}{15120}(-1279f_{0}+14428f_{1}-74376f_{2}+231600f_{3}-484554f_{4}+713160f_{5}-731388f_{6}+485616f_{7}-174735f_{8}+16444f_{9}+5084f_{10})-\frac{167}{2520}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{9})=\frac{1}{15120}(5084f_{0}-57203f_{1}+294048f_{2}-913236f_{3}+1909320f_{4}-2833362f_{5}+3061968f_{6}-2409108f_{7}+1324476f_{8}-454355f_{9}+72368f_{10})+\frac{2041}{7560}h^{11}f^{(11)}(\xi)$$
 * $$h^{4}f^{(4)}(x_{10})=\frac{1}{15120}(72368f_{0}-790964f_{1}+3923037f_{2}-11646672f_{3}+22968204f_{4}-31524696f_{5}+30600654f_{6}-20819472f_{7}+9531612f_{8}-2655764f_{9}+341693f_{10})+\frac{7645}{1512}h^{11}f^{(11)}(\xi)$$

11-punts 5e afgeleide:
 * $$h^{5}f^{(5)}(x_{0})=\frac{1}{288}(-8591f_{0}+72492f_{1}-278313f_{2}+640752f_{3}-979878f_{4}+1039656f_{5}-774402f_{6}+399408f_{7}-136347f_{8}+27788f_{9}-2565f_{10})+\frac{31063}{3024}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{1})=\frac{1}{288}(-2565f_{0}+19624f_{1}-68583f_{2}+144912f_{3}-205698f_{4}+205152f_{5}-145374f_{6}+72048f_{7}-23817f_{8}+4728f_{9}-427f_{10})+\frac{8261}{6048}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{2})=\frac{1}{288}(-427f_{0}+2132f_{1}-3861f_{2}+1872f_{3}+4002f_{4}-8424f_{5}+7878f_{6}-4464f_{7}+1593f_{8}-332f_{9}+31f_{10})-\frac{353}{3024}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{3})=\frac{1}{288}(31f_{0}-768f_{1}+3837f_{2}-8976f_{3}+12102f_{4}-10320f_{5}+5898f_{6}-2352f_{7}+651f_{8}-112f_{9}+9f_{10})-\frac{55}{6048}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{4})=\frac{1}{288}(9f_{0}-68f_{1}-273f_{2}+2352f_{3}-6006f_{4}+7944f_{5}-6162f_{6}+2928f_{7}-867f_{8}+156f_{9}-13f_{10})+\frac{67}{3024}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{5})=\frac{1}{288}(-13f_{0}+152f_{1}-783f_{2}+1872f_{3}-1938f_{4}+1938f_{6}-1872f_{7}+783f_{8}-152f_{9}+13f_{10})-\frac{139}{6048}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{6})=\frac{1}{288}(13f_{0}-156f_{1}+867f_{2}-2928f_{3}+6162f_{4}-7944f_{5}+6006f_{6}-2352f_{7}+273f_{8}+68f_{9}-9f_{10})+\frac{67}{3024}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{7})=\frac{1}{288}(-9f_{0}+112f_{1}-651f_{2}+2352f_{3}-5898f_{4}+10320f_{5}-12102f_{6}+8976f_{7}-3837f_{8}+768f_{9}-31f_{10})-\frac{55}{6048}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{8})=\frac{1}{288}(-31f_{0}+332f_{1}-1593f_{2}+4464f_{3}-7878f_{4}+8424f_{5}-4002f_{6}-1872f_{7}+3861f_{8}-2132f_{9}+427f_{10})-\frac{353}{3024}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{9})=\frac{1}{288}(427f_{0}-4728f_{1}+23817f_{2}-72048f_{3}+145374f_{4}-205152f_{5}+205698f_{6}-144912f_{7}+68583f_{8}-19624f_{9}+2565f_{10})+\frac{8261}{6048}h^{11}f^{(11)}(\xi)$$
 * $$h^{5}f^{(5)}(x_{10})=\frac{1}{288}(2565f_{0}-27788f_{1}+136347f_{2}-399408f_{3}+774402f_{4}-1039656f_{5}+979878f_{6}-640752f_{7}+278313f_{8}-72492f_{9}+8591f_{10})+\frac{31063}{3024}h^{11}f^{(11)}(\xi)$$

11-punts 6e afgeleide:
 * $$h^{6}f^{(6)}(x_{0})=\frac{1}{240}(7513f_{0}-67090f_{1}+270705f_{2}-650280f_{3}+1030290f_{4}-1125276f_{5}+858090f_{6}-451080f_{7}+156405f_{8}-32290f_{9}+3013f_{10})-\frac{781}{48}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{1})=\frac{1}{240}(3013f_{0}-25630f_{1}+98625f_{2}-226440f_{3}+344010f_{4}-361716f_{5}+266730f_{6}-136200f_{7}+46065f_{8}-9310f_{9}+853f_{10})-\frac{223}{60}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{2})=\frac{1}{240}(853f_{0}-6370f_{1}+21285f_{2}-42120f_{3}+55050f_{4}-50076f_{5}+32370f_{6}-14760f_{7}+4545f_{8}-850f_{9}+73f_{10})-\frac{13}{80}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{3})=\frac{1}{240}(73f_{0}+50f_{1}-2355f_{2}+9240f_{3}-18030f_{4}+21324f_{5}-16350f_{6}+8280f_{7}-2715f_{8}+530f_{9}-47f_{10})+\frac{17}{120}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{4})=\frac{1}{240}(-47f_{0}+590f_{1}-2535f_{2}+5400f_{3}-6270f_{4}+3684f_{5}-390f_{6}-840f_{7}+525f_{8}-130f_{9}+13f_{10})-\frac{13}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{5})=\frac{1}{240}(13f_{0}-190f_{1}+1305f_{2}-4680f_{3}+9690f_{4}-12276f_{5}+9690f_{6}-4680f_{7}+1305f_{8}-190f_{9}+13f_{10})-\frac{139}{12096}h^{12}f^{(12)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{6})=\frac{1}{240}(13f_{0}-130f_{1}+525f_{2}-840f_{3}-390f_{4}+3684f_{5}-6270f_{6}+5400f_{7}-2535f_{8}+590f_{9}-47f_{10})+\frac{13}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{7})=\frac{1}{240}(-47f_{0}+530f_{1}-2715f_{2}+8280f_{3}-16350f_{4}+21324f_{5}-18030f_{6}+9240f_{7}-2355f_{8}+50f_{9}+73f_{10})-\frac{17}{120}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{8})=\frac{1}{240}(73f_{0}-850f_{1}+4545f_{2}-14760f_{3}+32370f_{4}-50076f_{5}+55050f_{6}-42120f_{7}+21285f_{8}-6370f_{9}+853f_{10})+\frac{13}{80}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{9})=\frac{1}{240}(853f_{0}-9310f_{1}+46065f_{2}-136200f_{3}+266730f_{4}-361716f_{5}+344010f_{6}-226440f_{7}+98625f_{8}-25630f_{9}+3013f_{10})+\frac{223}{60}h^{11}f^{(11)}(\xi)$$
 * $$h^{6}f^{(6)}(x_{10})=\frac{1}{240}(3013f_{0}-32290f_{1}+156405f_{2}-451080f_{3}+858090f_{4}-1125276f_{5}+1030290f_{6}-650280f_{7}+270705f_{8}-67090f_{9}+7513f_{10})+\frac{781}{48}h^{11}f^{(11)}(\xi)$$

11-punts 7e afgeleide:
 * $$h^{7}f^{(7)}(x_{0})=\frac{1}{24}(-605f_{0}+5628f_{1}-23583f_{2}+58632f_{3}-95802f_{4}+107520f_{5}-83958f_{6}+45048f_{7}-15897f_{8}+3332f_{9}-315f_{10})+\frac{4781}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{1})=\frac{1}{24}(-315f_{0}+2860f_{1}-11697f_{2}+28392f_{3}-45318f_{4}+49728f_{5}-38010f_{6}+19992f_{7}-6927f_{8}+1428f_{9}-133f_{10})+\frac{1631}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{2})=\frac{1}{24}(-133f_{0}+1148f_{1}-4455f_{2}+10248f_{3}-15498f_{4}+16128f_{5}-11718f_{6}+5880f_{7}-1953f_{8}+388f_{9}-35f_{10})+\frac{301}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{3})=\frac{1}{24}(-35f_{0}+252f_{1}-777f_{2}+1320f_{3}-1302f_{4}+672f_{5}-42f_{6}-168f_{7}+105f_{8}-28f_{9}+3f_{10})-\frac{49}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{4})=\frac{1}{24}(3f_{0}-68f_{1}+417f_{2}-1272f_{3}+2310f_{4}-2688f_{5}+2058f_{6}-1032f_{7}+327f_{8}-60f_{9}+5f_{10})-\frac{19}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{5})=\frac{1}{24}(5f_{0}-52f_{1}+207f_{2}-408f_{3}+378f_{4}-378f_{6}+408f_{7}-207f_{8}+52f_{9}-5f_{10})+\frac{31}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{6})=\frac{1}{24}(-5f_{0}+60f_{1}-327f_{2}+1032f_{3}-2058f_{4}+2688f_{5}-2310f_{6}+1272f_{7}-417f_{8}+68f_{9}-3f_{10})-\frac{19}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{7})=\frac{1}{24}(-3f_{0}+28f_{1}-105f_{2}+168f_{3}+42f_{4}-672f_{5}+1302f_{6}-1320f_{7}+777f_{8}-252f_{9}+35f_{10})-\frac{49}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{8})=\frac{1}{24}(35f_{0}-388f_{1}+1953f_{2}-5880f_{3}+11718f_{4}-16128f_{5}+15498f_{6}-10248f_{7}+4455f_{8}-1148f_{9}+133f_{10})+\frac{301}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{9})=\frac{1}{24}(133f_{0}-1428f_{1}+6927f_{2}-19992f_{3}+38010f_{4}-49728f_{5}+45318f_{6}-28392f_{7}+11697f_{8}-2860f_{9}+315f_{10})+\frac{1631}{240}h^{11}f^{(11)}(\xi)$$
 * $$h^{7}f^{(7)}(x_{10})=\frac{1}{24}(315f_{0}-3332f_{1}+15897f_{2}-45048f_{3}+83958f_{4}-107520f_{5}+95802f_{6}-58632f_{7}+23583f_{8}-5628f_{9}+605f_{10})+\frac{4781}{240}h^{11}f^{(11)}(\xi)$$

11-punts 8e afgeleide:
 * $$h^{8}f^{(8)}(x_{0})=\frac{1}{3}(44f_{0}-422f_{1}+1821f_{2}-4656f_{3}+7812f_{4}-8988f_{5}+7182f_{6}-3936f_{7}+1416f_{8}-302f_{9}+29f_{10})-\frac{55}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{1})=\frac{1}{3}(29f_{0}-275f_{1}+1173f_{2}-2964f_{3}+4914f_{4}-5586f_{5}+4410f_{6}-2388f_{7}+849f_{8}-179f_{9}+17f_{10})-\frac{26}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{2})=\frac{1}{3}(17f_{0}-158f_{1}+660f_{2}-1632f_{3}+2646f_{4}-2940f_{5}+2268f_{6}-1200f_{7}+417f_{8}-86f_{9}+8f_{10})-3h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{3})=\frac{1}{3}(8f_{0}-71f_{1}+282f_{2}-660f_{3}+1008f_{4}-1050f_{5}+756f_{6}-372f_{7}+120f_{8}-23f_{9}+2f_{10})-\frac{1}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{4})=\frac{1}{3}(2f_{0}-14f_{1}+39f_{2}-48f_{3}+84f_{5}-126f_{6}+96f_{7}-42f_{8}+10f_{9}-f_{10})+\frac{1}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{5})=\frac{1}{3}(-f_{0}+13f_{1}-69f_{2}+204f_{3}-378f_{4}+462f_{5}-378f_{6}+204f_{7}-69f_{8}+13f_{9}-f_{10})+\frac{31}{360}h^{12}f^{(12)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{6})=\frac{1}{3}(-f_{0}+10f_{1}-42f_{2}+96f_{3}-126f_{4}+84f_{5}-48f_{7}+39f_{8}-14f_{9}+2f_{10})-\frac{1}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{7})=\frac{1}{3}(2f_{0}-23f_{1}+120f_{2}-372f_{3}+756f_{4}-1050f_{5}+1008f_{6}-660f_{7}+282f_{8}-71f_{9}+8f_{10})+\frac{1}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{8})=\frac{1}{3}(8f_{0}-86f_{1}+417f_{2}-1200f_{3}+2268f_{4}-2940f_{5}+2646f_{6}-1632f_{7}+660f_{8}-158f_{9}+17f_{10})+3h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{9})=\frac{1}{3}(17f_{0}-179f_{1}+849f_{2}-2388f_{3}+4410f_{4}-5586f_{5}+4914f_{6}-2964f_{7}+1173f_{8}-275f_{9}+29f_{10})+\frac{26}{3}h^{11}f^{(11)}(\xi)$$
 * $$h^{8}f^{(8)}(x_{10})=\frac{1}{3}(29f_{0}-302f_{1}+1416f_{2}-3936f_{3}+7182f_{4}-8988f_{5}+7812f_{6}-4656f_{7}+1821f_{8}-422f_{9}+44f_{10})+\frac{55}{3}h^{11}f^{(11)}(\xi)$$

11-punts 9e afgeleide:
 * $$h^{9}f^{(9)}(x_{0})=\frac{1}{2}(-11f_{0}+108f_{1}-477f_{2}+1248f_{3}-2142f_{4}+2520f_{5}-2058f_{6}+1152f_{7}-423f_{8}+92f_{9}-9f_{10})+12h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{1})=\frac{1}{2}(-9f_{0}+88f_{1}-387f_{2}+1008f_{3}-1722f_{4}+2016f_{5}-1638f_{6}+912f_{7}-333f_{8}+72f_{9}-7f_{10})+\frac{15}{2}h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{2})=\frac{1}{2}(-7f_{0}+68f_{1}-297f_{2}+768f_{3}-1302f_{4}+1512f_{5}-1218f_{6}+672f_{7}-243f_{8}+52f_{9}-5f_{10})+4h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{3})=\frac{1}{2}(-5f_{0}+48f_{1}-207f_{2}+528f_{3}-882f_{4}+1008f_{5}-798f_{6}+432f_{7}-153f_{8}+32f_{9}-3f_{10})+\frac{3}{2}h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{4})=\frac{1}{2}(-3f_{0}+28f_{1}-117f_{2}+288f_{3}-462f_{4}+504f_{5}-378f_{6}+192f_{7}-63f_{8}+12f_{9}-f_{10})+\frac{1}{4}h^{12}f^{(12)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{5})=\frac{1}{2}(-f_{0}+8f_{1}-27f_{2}+48f_{3}-42f_{4}+42f_{6}-48f_{7}+27f_{8}-8f_{9}+f_{10})-\frac{1}{2}h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{6})=\frac{1}{2}(f_{0}-12f_{1}+63f_{2}-192f_{3}+378f_{4}-504f_{5}+462f_{6}-288f_{7}+117f_{8}-28f_{9}+3f_{10})-\frac{1}{4}h^{12}f^{(12)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{7})=\frac{1}{2}(3f_{0}-32f_{1}+153f_{2}-432f_{3}+798f_{4}-1008f_{5}+882f_{6}-528f_{7}+207f_{8}-48f_{9}+5f_{10})+\frac{3}{2}h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{8})=\frac{1}{2}(5f_{0}-52f_{1}+243f_{2}-672f_{3}+1218f_{4}-1512f_{5}+1302f_{6}-768f_{7}+297f_{8}-68f_{9}+7f_{10})+4h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{9})=\frac{1}{2}(7f_{0}-72f_{1}+333f_{2}-912f_{3}+1638f_{4}-2016f_{5}+1722f_{6}-1008f_{7}+387f_{8}-88f_{9}+9f_{10})+\frac{15}{2}h^{11}f^{(11)}(\xi)$$
 * $$h^{9}f^{(9)}(x_{10})=\frac{1}{2}(9f_{0}-92f_{1}+423f_{2}-1152f_{3}+2058f_{4}-2520f_{5}+2142f_{6}-1248f_{7}+477f_{8}-108f_{9}+11f_{10})+12h^{11}f^{(11)}(\xi)$$

11-punts 10e afgeleide:
 * $$h^{10}f^{(10)}(x_{0})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-5h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{1})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-4h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{2})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-3h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{3})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-2h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{4})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{5})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}-\frac{5}{12}h^{12}f^{(12)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{6})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}+h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{7})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}+2h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{8})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}+3h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{9})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}+4h^{11}f^{(11)}(\xi)$$
 * $$h^{10}f^{(10)}(x_{10})=f_{0}-10f_{1}+45f_{2}-120f_{3}+210f_{4}-252f_{5}+210f_{6}-120f_{7}+45f_{8}-10f_{9}+f_{10}+5h^{11}f^{(11)}(\xi)$$