User:Mrconter1/sandbox

Example
Thus, if the function $$f $$ and vector $$\mathbf{v} $$ is defined as:


 * $$f(\mathbf{x}, \mathbf{y}) = x^2 + y^2$$

and:


 * $$\mathbf{v} = (1, 2), |\mathbf{v}| = \sqrt{1^2+2^2} = \sqrt{5}$$

The directional derivative will be:

$$\nabla_{\mathbf{v}}{f} = \frac{\partial{f}}{\partial{\mathbf{x}}} \cdot \frac{\mathbf{v_x}}{|\mathbf{v}|} + \frac{\partial{f}}{\partial{\mathbf{y}}} \cdot \frac{\mathbf{v_y}}{|\mathbf{v}|} = 2x \cdot \frac{1}{\sqrt{5}} + 2y \cdot \frac{2}{\sqrt{5}}$$