# How do you find the derivative of f(x) = x^3e^x?

Oct 27, 2016

$f ' \left(x\right) = 3 {x}^{2} {e}^{x} + {x}^{3} {e}^{x}$
You need to use the product rule; $\frac{d}{\mathrm{dx}} \left(u v\right) = u \frac{\mathrm{dv}}{\mathrm{dx}} + v \frac{\mathrm{du}}{\mathrm{dx}}$
$f \left(x\right) = {x}^{3} {e}^{x}$
$\therefore f ' \left(x\right) = {x}^{3} \frac{d}{\mathrm{dx}} {e}^{x} + {e}^{x} \frac{d}{\mathrm{dx}} {x}^{3}$
$\therefore f ' \left(x\right) = {x}^{3} {e}^{x} + {e}^{x} \left(3 {x}^{2}\right)$
$\therefore f ' \left(x\right) = 3 {x}^{2} {e}^{x} + {x}^{3} {e}^{x}$