Let $f ( x , y ) = x ^ { 2 } e ^ { y }$

Essay

Let $f ( x , y ) = x ^ { 2 } e ^ { y }$ and $P ( - 2,0 )$ .(a) Find the rate of change in the direction of $\nabla f ( P )$ .(b) Calculate $D _ { u } f ( P )$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 135 ^ { \circ }$ with $\nabla f ( P )$ .