The scalar field $f(r,\phi,z) = rcos^2\phi + zsin\phi$ is given. Calculate:
(a) The gradient of $f(r,\phi,z)$ in cylindrical coordinates.
(b) The gradient of $f(r,\phi,z)$ in Cartesian coordinates.
(c) The gradient of $f(r,\phi,z)$ in spherical coordinates.