Question

If $f\left(x\right)=\log \left(\log x\right),$ find $f^{\prime }\left(x\right)$

Answer 1

$f\left(x\right)=\log \left(x\right)$

$\Rightarrow f^{\prime }\left(x\right)=\frac{1}{\log x}.\frac{1}{x}=\frac{1}{x\left(\log x\right)}$

Hence, the answer is $\frac{1}{x\left(\log x\right)}.$