Question

How do you differentiate `f(x)=(5e^x+cosx)(x-2)` using the product rule?

Answer 1

`=5xe^x-5e^x-xsinx+2sinx+cosx`

Explanation:

If `f(x)=g(x)*h(x)`, you know that

`f'(x)=g'(x)*h(x)+g(x)*h'(x)` (product rule), then

`f'(x)=(5e^x-sinx)(x-2)+(5e^x+cosx)*1`

`=5xe^x-xsinx-10e^x+2sinx+5e^x+cosx`

`=5xe^x-5e^x-xsinx+2sinx+cosx`