Question

Differentiate the given function w.r.t. $x$.
$\log \left(\log x\right),x>1$

Answer 1

Let $y=\log \left(\log x\right)$
Thus using chain rule,
$\frac{dy}{dx}=\frac{d}{dx}\left[\log \right(\log x\left)\right]$
$=\frac{1}{\log x}.\frac{d}{dx}\left(\log x\right)$
$=\frac{1}{\log x}.\frac{1}{x}$
$=\frac{1}{x\log x},x>1$