Answer
$$ y'= \frac{3}{x\ln x}.$$
Work Step by Step
Recall that $(\ln x)'=\dfrac{1}{x}$
Since $ y=\ln (\ln x)^3$, first we simplify $ y $ as follows
$$ y=3\ln (\ln x)$$
then by the chain rule, we have
$$ y'=3\frac{1/x}{\ln x}=\frac{3}{x\ln x}.$$
