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

Explanation

1. 01

   Outside $\sin u$, inside $u = \log x$, $u' = \frac{1}{x}$.

2. 02

   $\cos(\log x) \cdot \frac{1}{x} = \frac{\cos(\log x)}{x}$.