Electrical Potential to Electrical Field

Question

If the electrical potential is V=x³y² Volt at any point of an cartesian coordinate system, what is the electrical field at (x,y,z)=(4,2,1) metres.

a) -192i -256j -12k

b) 0

c) -192i -256j

d) -64y²i -4x³j

e) -64x³i -192y²j

I think the answer is "d)" but I can't be sure.

Answer 1

E_x = -∂V/∂x = -3x²y²

E_y = -∂V/∂y = -2x³y

E_z = 0 since V does not depend on z

Now plug in x=4 and y=2 and get

E_x = -3(4)²(2)² = -192 volts/m

E_y = -2(4)³(2) = -256 volts/m

Answer (c) is correct.