Answer
a)$\nabla f=<2xyz-yz^3, x^2z-xz^3,x^2y-3xyz^2>$
b)$\nabla f_{(2, -1, 1)}=<-3, 2, 2>$
c)$D_uf_{(2, -1, 1)}=\frac{2}{5}$
Work Step by Step
$\nabla f=<2xyz-yz^3, x^2z-xz^3,x^2y-3xyz^2>$
$\nabla f_{(2, -1, 1)}=<-3, 2, 2>$
$D_uf_{(2, -1, 1)}=\nabla f_{(2, -1, 1)}\cdot u=<-3, 2, 2>\cdot<0, \frac{4}{5}, -\frac{3}{5}>=\frac{2}{5}$
