Chapter 13.6, Problem 79ES

If the electric potential at a point $\left(x,y\right)$ in the $xy\text{-plane}$ is $V\left(x,y\right),$ then the electric intensity vector at the point $\left(x,y\right)\text{is}\text{E}=-\nabla V\left(x,y\right).$ Suppose that $V\left(x,y\right)=e^{-2x}\cos 2y.$

(a) Find the electric intensity vector at $\left(\pi /4,0\right).$

(b) Show that at each point in the plane, the electric potential decreases most rapidly in the direction of the vector $\text{E}\text{.}$