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

Nov 19, 2015

Actually, there's no need to use the product rule here: you have written $x \left({e}^{2} - 1\right)$, and you can derive it to get ${e}^{2} - 1$ immediately.

Maybe there's a mistake and you meant $x \cdot {e}^{x}$?

In that case, the product rule states that

$\left(f \cdot g\right) ' = f ' g + f g '$

So, we have

$f ' g + f g ' = 1 \cdot {e}^{x} + x \cdot {e}^{x} = {e}^{x} \left(1 + x\right)$

And the whole derivative would thus be ${e}^{x} \left(1 + x\right) - 1$