Problem 20.21

20.21. a)
If the potential is given by
V = 5x - 3x²y + 2yz²
then to find the components of the electric field, we take derivatives in the various space variables.
$E_{x} = -\frac{\partial V}{\partial x} ~=~ -5 + 6xy$
$E_{y} = -\frac{\partial V}{\partial y} ~=~ 3x^{2} -2z^{2}$
$E_{z} = -\frac{\partial V}{\partial z} ~=~ -4yz$
So, evaluated at the point (1,0,-2), we find that the electric field has the value
$\vec{E} = (-5,-5,0)$