Answer
$$ y'= 3\cosh^2x \sinh x \cosh( \cosh^3 x) .$$
Work Step by Step
Recall that $(\sinh x)'=\cosh x$
Recall that $(\cosh x)'=\sinh x$
Since $ y=\sinh (\cosh^3 x)$, then the derivative, by using the chain rule, is given by
$$ y'=\cosh( \cosh^3 x) ( \cosh^3 x)'=3\cosh^2x \sinh x \cosh( \cosh^3 x) .$$
