# What is the derivative of xe^x?

Dec 17, 2014

To evaluate this derivative you use the product rule .

When you have a function that is the product of 2 functions $f \left(x\right)$ and $g \left(x\right)$ you can derive it as:

$\frac{d}{\mathrm{dx}} f \left(x\right) g \left(x\right) = f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

$f \left(x\right) = x \mathmr{and} f ' \left(x\right) = 1$
$g \left(x\right) = {e}^{x} \mathmr{and} g ' \left(x\right) = {e}^{x}$
$\frac{d}{\mathrm{dx}} x {e}^{x} = 1 {e}^{x} + x {e}^{x} = {e}^{x} \left(x + 1\right)$