Answer
$$\frac{ \cosh x}{\sqrt{\sinh^2x-1}} $$
Work Step by Step
Given $$y=\cosh^{-1}(\sinh x)$$
Let $u=\sinh x$, then
$$y=\cosh^{-1}(u)$$
and
\begin{align*}
\frac{dy}{dx}&=\frac{1}{\sqrt{u^2-1}} \frac{du}{dx}\\
&=\frac{1}{\sqrt{u^2-1}} \cosh x\\
&=\frac{ \cosh x}{\sqrt{\sinh^2x-1}}
\end{align*}
