Question

If $y=lo{g}_7\left(logx\right)$ find $\frac{dy}{dx}$.

Answer 1

$y=lo{g}_{7}lo{g}_x$

$y=\frac{lo{g}_{e}lo{g}_x}{lo{g}_{e}7}$

$\frac{dy}{dx}=\frac{1}{lo{g}_{e}7}\left(\frac{1}{lo{g}_x}\right)\frac{d}{dx}logx$

$\frac{dy}{dx}=\frac{1}{lo{g}_{e}7}\frac{1}{logx}.\frac{1}{x}$

$\frac{dy}{dx}=\frac{1}{lo{g}_{e}7xlogx}$

$\therefore \frac{dy}{dx}=\frac{1}{lo{g}_{e}7xlogx}$