Study guide and 4 practice problems on:

Directional derivative definition

The directional derivative of a function $f(x,y)$ is the rate of change of $f$ if $(x,y)$ is changed in the direction of $\bfv$.
Let $\bfx = (x,y)$. Then, $$D_\bfv f(\bfx) = \lim_{\epsilon \to 0} \frac{f(\bfx + \epsilon \bfv/|\bfv|) - f(\bfx)} {\epsilon}$$