Calculus: Early Transcendentals 8th Edition

$$f'(x)=e^x(\cosh x+\sinh x)$$
$f'(x)=\frac{d}{dx}e^x \cosh x$ Using the product rule: $f'(x)=\cosh x\times\frac{d}{dx}e^x+e^x\times \frac{d}{dx}\cosh x$ $=e^x \cosh x+e^x\sinh x$ $=e^x(\cosh x+\sinh x)$