What is $\frac{d}{dx}\left(\log 5x\right)$ for $x > 0$?

Explanation

1. 01

   $\log 5x = \log 5 + \log x$, and $\log 5$ is a constant.

2. 02

   So the derivative is $0 + \frac{1}{x} = \frac{1}{x}$; the chain rule agrees: $\frac{5}{5x} = \frac{1}{x}$.