Key concept to solve this:
Potential Energy Function: If a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case satisfies the derivative condition
-dU/dx = F(x)
We have given U = 20xy/ z
Now taking the derivative of U w.r.t x,y and z we get,
Fx = -20y/z, Fy = -20x/z, and Fz = 20xy/z2
Now adding all we get the final force, i.e
F = -(20y/z)i-(20x/z)j+(20xy/z2)k.