It is given that f(x,y,z)=xy4ze+35. Here
fx(x,y,z)=y,
fx(x,y,z)=x,
fx(x,y,z)=-4e.

Now we know that gradient of f at a point (x,y,z) is given by \(\displaystyle▽{f}={\left({f}{x}{\left({x},{y},{z}\right)},{f}{y}{\left({x},{y},{z}\right)},{f}{z}{\left({x},{y},{z}\right)}\right)}.\)

Therefore, PSK▽f(3,-3,2)=(fx(3,-3,2),fy(3,-3,2),fz(3,-3,2)) =(-3,3,-4e).ZSK

Now we know that gradient of f at a point (x,y,z) is given by \(\displaystyle▽{f}={\left({f}{x}{\left({x},{y},{z}\right)},{f}{y}{\left({x},{y},{z}\right)},{f}{z}{\left({x},{y},{z}\right)}\right)}.\)

Therefore, PSK▽f(3,-3,2)=(fx(3,-3,2),fy(3,-3,2),fz(3,-3,2)) =(-3,3,-4e).ZSK