Solution
= Solution
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. Hence
$$
\boxed{\nabla(1/r)=-\frac{r}{r^3}.}
$$
On the right the numerator denotes the position vector, while its denominator is the cube of its magnitude.