Does Fx y z 2xyz i x2 z j x2 y 4z k represent a conserva

Does F(x, y, z) = 2xyz i + x^2 z, j + (x^2 y + 4z) k represent a conservative force field? If so, determine phi in F = grad phi.

Solution

Finding delA/delx , and delA/dely and checking whether they are equal gives us whether or not F represents a conservative force field

delA/delx = 2yz +2xz+2xy

delA/dely = 2xz +0 +x^2 +0

again they are not equal , so do not represent conservative force field