Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 2

$\frac{1}{x}$

Using the log rule $$\log\left(\frac{a}{b}\right)=\log(a)-\log(b)$$ we can write $\ln\left(\frac{x}{3}\right)$ as $$\ln\left(\frac{x}{3}\right)=\ln x-\ln 3.$$ Taking the derivative of this expression yields $$\frac{d}{dx}\left(\ln\left(\frac{x}{3}\right)\right)=\frac{d}{dx}(\ln x-\ln 3)=\frac{1}{x}.$$