Question

How do you differentiate `f(x)=xe^(-2x)` using the product rule?

Answer 1

`f'(x)=e^(-2 x)(1-2 x)`

Explanation:

`f(x) = x e^(-2 x)` ; Product rule: `(f g)' = f'g+f g'`

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

`f'(x)=e^(-2 x)-2 x e^(-2 x)` or

`f'(x)=e^(-2 x)(1-2 x)` [Ans]