Talk:Sum rule in differentiation

i think the math in this artcile should be formatted corectly... only problem is i don't know how to do it

add concrete examples and references
can we add concrete examples to the calc pages. at least two for each concept to make them useful to the average user? And this page still needs references. I will add them but Im new so I will need a little help formatting them. aharon42 (talk) 13:15, 6 September 2008 (UTC)

The actual proof?
Consider we differentiate this function y = u + v, where u and v are functions.

I let u = f(x) and v = g(x).

y = f(x) + g(x)

dy/dx = lim{m→0} [f(x+m)+g(x+m)-(f(x)+g(x))]/m

= lim{m→0} [f(x+m)-f(x)+g(x+m)-g(x)]/m

= lim{m→0} [(f(x+m)-f(x))/m+(g(x+m)-g(x))/m]

= f'(x) + g'(x)

= du/dx + dv/dx

This gives the clear proof of this without the use of the "∆x division". Garygoh884 (talk) 10:57, 25 May 2011 (UTC)