Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics V resit / Question 2 / a / ii / Solution

For $r>0$, the chain rule gives $\partial r/\partial x_i=x_i/r$. Applying the product rule to the components of the vector field yieldsThe calculation is pointwise away from the origin; any extension of the vector field to the origin must be considered separately.