In cylindrical polar coordinates, a scalar field g and a vector field G are given as: g(p, o, z) = exp(-p²) sin(z) and G(p, o, z) = exp(-p²) (-2p sin(z)p+ cos(z) 2). Show that g is the potential field for G. Find the divergence and curl of G. You do not need to know the formula for curl in cylindrical coordinates to answer this question.