Answer
$y' = \dfrac{2\sin(\ln x) \cos(\ln x)}{x}$
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
$f(u) = u^2$
$u = \sin(\ln x)$
Derivate the function:
$f'(u) = 2uu'$
Now let's find u'
*Note: Here you have to apply the chain rule again
$u' = \dfrac{\cos(\ln x)}{x}$
Then undo the substitution, simplify and get the answer:
$y' = \dfrac{2\sin(\ln x) \cos(\ln x)}{x}$