Past exam of the mathematics course of the University of Cambridge / 2014 / ia / Paper 3 / 3A / b / i / Solution

Apply the product rule and the preceding gradient formula to the vector field $F_i=f(r)x_i$. Summing over the repeated index givesHere ${\delta }_{ii}=n$ for the Kronecker delta. Thus the divergence and curl of a radial vector field give, in any dimension,