Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 24

$\displaystyle \frac{2x-1}{x^{2}-x}$

(see p. 838, Generalized Rule)$\quad$ $\displaystyle \frac{d}{dx}[\ln|u|]=\frac{1}{u}\cdot\frac{du}{dx}$ $u(x)=x^{2}-x$ $\displaystyle \frac{du}{dx}=2x-1$ $\displaystyle \frac{d}{dx}[\ln|2x^{2}+1|]=\frac{1}{x^{2}-x}\cdot(2x-1)$ $=\displaystyle \frac{2x-1}{x^{2}-x}$