Answer
$y' = \dfrac{1}{2x\sqrt{\ln x}}$
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) =\sqrt{u} $
$u = \ln x$
Derivate the function:
$f'(u) = \dfrac{u'}{2\sqrt{u}}$
Now let's find u'
$u' = \dfrac{1}{x}$
Then undo the substitution, simplify and get the answer:
$f'(x) = \dfrac{1}{2x\sqrt{\ln x}}$