Chapter 11 - Section 11.5 - Derivatives of Logarithmic and Exponential Functions - Exercises - Page 842: 4

$\displaystyle \frac{1}{x\ln 3}$

$\quad$ $\displaystyle \frac{d}{dx}[\log_{b}u]=\frac{\mathrm{l}}{u\ln b}\frac{du}{dx}$ $b=3$ $u(x)=x$ $\displaystyle \frac{du}{dx}=1$ $ \displaystyle \frac{d}{dx}[\log_{3}(x)]=\frac{\mathrm{l}}{(x)\ln 3}\cdot 1 =\displaystyle \frac{1}{x\ln 3}$