Question

If $y={\log }_5\left({\log }_{7}x\right)$, find $\frac{dy}{dx}$

Answer 1

$y={\log }_5\left({\log }_{7}x\right)$

$\Rightarrow \frac{dy}{dx}=\frac{1}{{\log }_{7}x{\log }_{e}5}\times \frac{1}{x{\log }_{e}7}$

$=\frac{1}{x{\log }_{7}x{\log }_{e}5.{\log }_{e}7}$