Question

Find the derivative. f(x) = e^(x) cosh(x)

Answer 1

We are given

$f(x)=e^{x} cosh(x)$

Since, $e^{x}$ and $cosh(x)$ are multiplied

so, we will use product rule of derivative

$\mathrm{Apply\:the\:Product\:Rule}:\quad \left(f\cdot g\right)'=f\:'\cdot g+f\cdot g'$

$f'(x)=\frac{d}{dx}\left(e^x\right)\cosh \left(x\right)+\frac{d}{dx}\left(\cosh \left(x\right)\right)e^x$

we know that

$\frac{d}{dx}\left(e^x\right)=e^x$

and

$\frac{d}{dx}\left(\cosh \left(x\right)\right)=\sinh \left(x\right)$

so, we can plug these values

and we get

$f'(x)=e^x\cosh \left(x\right)+\sinh \left(x\right)e^x$...............Answer