Gradient Vector

Theorem: $\nabla w\perp$ level curve
$\nabla w=<\frac{\partial w}{\partial x},\frac{\partial w}{\partial y}>$
Pointing to higher value of the function
By Chain Rule: $\frac{dw}{dt}=\nabla w\cdot \frac{d\vec{r}}{dt}=\nabla w\cdot \vec{v}$
Tex