Consider the function $f(x,y,z)=xy+y{z}^2+x{z}^3.$ Find the gradient of $f$ :

Find the gradient of $f$ at the point $(3,-2,-1).$

Find the rate of change of the function $f$ at the point $(3,-2,-1)$ in the direction $u=($:$\frac{2}{\sqrt[\phantom{2}]{17}},\frac{3}{\sqrt[\phantom{2}]{17}},\frac{2}{\sqrt[\phantom{2}]{17}}$:$).$