Chapter 6.12, Problem 12MP

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

(a) $\nabla u$ at $(0,1,2)$;

(b) the directional derivative of $u$ at $(0,1,2)$ in the direction $2i+2j-k$;

(c) the equations of the tangent plane and of the normal line to the level surface $u=2$ at $(0,1,2)$;

(d) a unit vector in the direction of most rapid increase of $u$ at $(0,1,2)$.