Gradient for Functions of the Radius

For a function fdefined in terms of spherical radial coordinatewe can write

In spherical polar coordinates

\[f\]

is not a function of

\[\theta\]

or

\[\phi\]

so

Example: Ifthen

Example: Ifthen

\[\mathbf{\nabla} f = - \frac{1}{r^2} \mathbf{e}_r\]