Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2007 / Paper 1 / 1 / i

Away from the origin, $\hat{\mathbf{r}}=\nabla r$. Hence the curl of a gradient gives $\nabla \times \hat{\mathbf{r}}=0$. Its divergence is the Laplacian of the radial coordinate, which in spherical coordinates isEquivalently, differentiating $x_i/r$ in Cartesian coordinates gives $3/r-r^2/r^3=2/r$.