# How do you find the derivative of (x^2)(e^x)?

Jul 27, 2018

${e}^{x} \left({x}^{2} + 2 x\right)$

#### Explanation:

Let $f \left(x\right) = {x}^{2}$ and $g \left(x\right) = {e}^{x}$. Since we have a product of functions, the derivative can be found with the Product Rule

$f ' \left(x\right) g \left(x\right) + f \left(x\right) g ' \left(x\right)$

From some basic derivatives, we know $f ' \left(x\right) = 2 x$ and $g ' \left(x\right) = {e}^{x}$. We can now plug these into the Product Rule to get

$2 x {e}^{x} + {x}^{2} {e}^{x}$

We can factor out an ${e}^{x}$ to get

${e}^{x} \left({x}^{2} + 2 x\right)$

Hope this helps!