Example: $3$

$(a)$ Find the directional derivative $off(x,y,z)=x^{2}y-y{z}^3+zat$ the point $(-1,-2,1)in$ the

direction $of$ the vector $a=2i+j-2k.$

$(b)$ Let $f(x,y)=x^2{e}^y.$ Find the maximum value $of$ a directional derivative $at(-3,2),$ and find the

unit vector $in$ the direction $in$ which the maximum value occurs.

$(c)$ Find the directional derivative $off(x,y)=e^{xy}at(-2,-1)in$ the direction $of$ the negative

$y-$axis.