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)=(d)/(dx)\left(e^x\right)\cosh \left(x\right)+(d)/(dx)\left(\cosh \left(x\right)\right)e^x`

we know that

`(d)/(dx)\left(e^x\right)=e^x`

and

`(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