Answer
$y'=\dfrac{\cosh x}{\sqrt{\sinh^{2}x-1}}$
Work Step by Step
$y=\cosh^{-1}(\sinh x)$
Start the differentiation process by using the chain rule:
$y'=\dfrac{1}{\sqrt{\sinh^{2}x-1}}(\sinh x)'=...$
Evaluate the remaining derivative and simplify:
$...=\dfrac{\cosh x}{\sqrt{\sinh^{2}x-1}}$
