Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 48

$r^{\prime}(x)=\displaystyle \frac{1+e^{x}}{x+e^{x}}$

With $u(x)=x+e^{x}$, $r(x)=$ logarithm of an absolute value of a function, $r^{\prime}(x)=\displaystyle \frac{d}{dx}[\ln|u|]=\frac{1}{u}\cdot\frac{du}{dx}$ $\displaystyle \frac{du}{dx}=1+e^{x}$ So, $r^{\prime}(x)=\displaystyle \frac{1}{x+e^{x}}\cdot(1+e^{x})$ $r^{\prime}(x)=\displaystyle \frac{1+e^{x}}{x+e^{x}}$