Question

How do you differentiate `f(x)=e^x*sinx` using the product rule?

Answer 1

`f'(x) = e^xcosx + e^xsinx`

Explanation:

Use the product rule `d/dx(uv)=u(dv)/dx + v(du)/dx`

So, with `f(x)=e^xsinx` we have:

`f'(x) = e^xd/dxsinx+ sinxd/dxe^x`
`:. f'(x) = e^xcosx+ sinxe^x`
`:. f'(x) = e^xcosx + e^xsinx`