Chapter 6.12, Problem 10MP

Given $u=xy+\sin z,$ find

(a) the gradient of $u$ at $(1,2,\pi /2)$;

(b) how fast $u$ is increasing, in the direction $4i+3j,$ at $(1,2,\pi /2)$;

(c) the equation of the tangent plane to the surface $u=3$ at $(1,2,\pi /2)$.