Deriving the divergence in cylindrical coordinates using the Jacobian

thealyosha

I am trying to derive the divergence in cylindrical coordinates using the Jacobian. I have already found the Jacobian (3x3 matrix taking derivatives of (r, phi, z) with respect to (x, y, z)), but I am not sure what to do from there.

I think I somehow find the gradient in cylindrical from the Jacobian, then use that to find the divergence? Help is appreciated. Thanks.