Solution
= Solution
Away from the origin, $\hat{\mathbf r}=\nabla r$. Hence the <curl of a gradient> gives $\nabla\times\hat{\mathbf r}=\mathbf0$. Its <divergence> is the <Laplacian> of the radial coordinate, which in <spherical coordinates> is
$$
\boxed{\nabla\cdot\hat{\mathbf r}=\nabla^2r=\frac1{r^2}\frac{d}{dr}(r^2)=\frac2r,\qquad r>0.}
$$
Equivalently, differentiating $x_i/r$ in <Cartesian coordinates> gives $3/r-r^2/r^3=2/r$.