Let $f ( x , y , z ) = x ^ { 2 } y - y z ^ { 3 } + z$

Essay

Let $f ( x , y , z ) = x ^ { 2 } y - y z ^ { 3 } + z$ and $P ( 1 , - 2,0 )$ . Calculate $D _ { u } f ( P )$ where $\mathbf { u }$ is a unit vector making an angle $\theta = 45 ^ { \circ }$ with $\nabla f ( P )$ .