Answer
$$ y'= \frac{1}{x}\cosh (\ln x).$$
Work Step by Step
Recall that $(\ln x)'=\dfrac{1}{x}$
Recall that $(\cosh x)'=\sinh x$
Since $ y=\sinh (\ln x) $, then the derivative, by using the chain rule, is given by
$$ y'=\cosh (\ln x) (\ln x)'= \frac{1}{x}\cosh (\ln x).$$
