Answer
$f'(x) = \dfrac{1}{x\ln x}$
Work Step by Step
In order to derivate this function you have to apply the chain rule
Let's make a «u» substitution to make it easier
$f(u) = \ln (u)$
$u = \ln (u)$
Derivate the function:
$f'(u) = \dfrac{u'}{u}$
Now let's find u'
$u' = \dfrac{1}{x}$
Then undo the substitution, simplify and get the answer:
$f'(x) = \dfrac{1}{x\ln x}$
