Answer
$\frac{2}{x} \ln x$
Work Step by Step
$y= (\ln x)^{2}$
Let us substitute $t= \ln x$
Then, $y= t^{2}$
According to the chain rule,
$\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}= 2t\times\frac{1}{x}$
Undoing substitution, we obtain
$\frac{dy}{dx}= \frac{2}{x} \ln x$
