Answer
$y'=3e^{\cosh 3x}\sinh (3x)$
Work Step by Step
Given: $y=e^{\cosh 3x}$
Now, $y'=\dfrac{d}{dx}[e^{\cosh 3x}]$
Apply chain rule.
$y'=(\dfrac{de^{\cosh 3x}}{d\cosh 3x})(\dfrac{d\cosh 3x}{d3x})
(\dfrac{d(3x)}{dx})$
or, $=e^{\cosh 3x}(\sinh 3x)(3)$
Thus $y'=3e^{\cosh 3x}\sinh (3x) $