What is $\frac{d}{dx}\left(\log{\left(\log x \right)}\right)$ for $x > 1$?

Explanation

1. 01

   Outside $\log u$, inside $u = \log x$: $\frac{1}{u} \cdot \frac{1}{x}$.

2. 02

   $\frac{1}{x\log x}$.