Differentiate with respect to $x$ the following function: $\log _{7}(\log x)$

(N/A) Let $y = \log _{7}(\log x) = \frac{\log (\log x)}{\log 7}$ (by change of base formula).
The function is defined for all real numbers $x > 1$. Therefore,
$\frac{dy}{dx} = \frac{1}{\log 7} \frac{d}{dx}(\log (\log x))$
$= \frac{1}{\log 7} \cdot \frac{1}{\log x} \cdot \frac{d}{dx}(\log x)$
$= \frac{1}{\log 7} \cdot \frac{1}{\log x} \cdot \frac{1}{x}$
$= \frac{1}{x \log x \log 7}$