Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 37

$ \displaystyle \frac{\mathrm{l}}{\ln 2(x+1)}$

Apply $\displaystyle \frac{d}{dx}[\log_{b}u]=\frac{\mathrm{l}}{u\ln b}\frac{du}{dx} \quad $(see p. 836) $\displaystyle \frac{d}{dx}[\log_{2}(x+1)]=\frac{\mathrm{l}}{(x+1)\ln 2}\cdot 1$ $=\displaystyle \frac{\mathrm{l}}{\ln 2(x+1)}$