Vx y z 5x2 2xy yz Ex y z SolutionE dVdrrcap rcap is dir

V(x, y, z) = 5x^2 + 2xy + yz E(x, y, z) = ?

E = (-dV/dr)*(rcap)

rcap is direction of electric field as electric field is vector quantity

Ex = (-dV/dx)*i = -d(5x^2+2xy+yz)/dx

Ex = (-10x -2y) i

Ey = (-dV/dy)*j = -d(5x^2+2xy+yz)/dy = (-2x - z) j

Ez = (-dV/dz)*k = -d(5x^2+2xy+yz)/dz = (-y) k

E(x,y,z) = (-10x - 2y)i + (-2x - z)j + (-y)k

Let me know if you have any doubt.