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

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

#### Work Step by Step

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*}

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