Thank you for reporting, we will resolve it shortly
Q.
If $y=\log _7(\log x)$, then $\frac{d y}{d x}$ is equal to
Continuity and Differentiability
Solution:
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{d y}{d x}=\frac{1}{\log 7} \frac{d}{d x}(\log (\log x))$
$=\frac{1}{\log 7} \frac{1}{\log x} \cdot \frac{d}{d x}(\log x)=\frac{1}{x \log 7 \log x}$