Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 16 / a / ii

For $r=\sqrt{x^2+y^2+z^2}>0$, the chain rule gives ${\partial }_x(r^{-1})=-x/r^3$, with analogous formulas for the other components. HenceOn the right the numerator denotes the position vector, while its denominator is the cube of its magnitude.