Question

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

Answer 1

`f'(x)=(5e^x+sec^2x)(x^2-2x)+(5e^x+tanx)(2x-2)`

Explanation:

For `f(x)=(5e^x+tanx)(x^2-2x)`, we find `f'(x)` by doing:

`f'(x)=d/dx[5e^x+tanx] (x^2-2x)+(5e^x+tanx)d/dx[x^2-2x]`

`f'(x)=(5e^x+sec^2x)(x^2-2x)+(5e^x+tanx)(2x-2)`