Calculating gradf in spherical polar basis?

Question

If $f(\mathbf{r})=\vert\mathbf{r}\vert^4$

How would you calculate $\operatorname{grad} f$ in spherical polar basis?

Answer 1

Hint:

Take advantage of the fact that $|\vec r|=r$; and $g'(r)=4r^3$ for $g(r)=r^4$.

For the whole story, you can read: https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates