# Directional Derivatives

The directional derivative of $f(x,y)$ in the direction of a unit vector $u=(u_{1},u_{2})$ at the point $a=(a,b)$ is denoted by D_\vec{u}f(a,b) and defined as

D_\vec{u}f(a,b) = \lim_{h \to 0}\frac{f(a+hu_1, b+hu_2)-f(a,b)}{h}

In practice, we can use D_\vec{u}f(a,b) = \nabla f(a,b) \cdot \vec{u}