Chapter 15 - Differentiation in Several Variables - 15.6 The Chain Rule - Exercises - Page 809: 35

$$ \frac{-1}{r^3}\mathbf{r}$$

Since $$F(r)= \frac{1}{r},\ \ \ \ \ \ \ \ F'(r) = \frac{-1}{r^2} $$ Then \begin{align*} \nabla f &=F^{\prime}(r) e_{\mathbf{r}}\\ &= \frac{-1}{r^2}e_{\mathbf{r}}\\ &= \frac{-1}{r^2}\frac{\mathbf{r}}{r}\\ &=\frac{-1}{r^3}\mathbf{r} \end{align*}