Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 5

$\displaystyle \frac{2x}{x^{2}+3}$

$\quad$ $\displaystyle \frac{d}{dx}[\ln|u|]=\frac{1}{u}\cdot\frac{du}{dx}$ $u(x)=x^{2}+3$ $\displaystyle \frac{du}{dx}=2x$ $\displaystyle \frac{d}{dx}[\ln|x^{2}+3|]=\frac{1}{x^{2}+3}\cdot 2x=\frac{2x}{x^{2}+3}$