Answer
$\dfrac{1}{x \ln x}$
Work Step by Step
We have: $f(x)=\ln |ln x|$
We differentiate both sides with respect to $x$.
$f^{\prime}(x)=\dfrac{d}{dx} [\ln |ln x|] \\=\dfrac{1}{\ln x} \dfrac{d}{dx} [\ln (x)]\\= \dfrac{1}{\ln x} \times \dfrac{d}{dx}(\dfrac{1}{x} )$
Simplify to obtain:
$f^{\prime}(x)=\dfrac{1}{x \ln x}$
