# How do you find the derivative of f(x)= (x^3)(e^(2x))?

Mar 31, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{2} {e}^{2 x} \left(3 + 2 x\right)$

#### Explanation:

Product rule

$\frac{d}{\mathrm{dx}} \left[u v\right] = \frac{\mathrm{du}}{\mathrm{dx}} v + \frac{\mathrm{dv}}{\mathrm{dx}} u$

$u = {x}^{3}$
$v = {e}^{2 x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left[{x}^{3}\right] {e}^{2 x} + \frac{d}{\mathrm{dx}} \left[{e}^{2 x}\right] {x}^{3}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2} {e}^{2 x} + 2 {e}^{2 x} {x}^{3}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{2} {e}^{2 x} \left(3 + 2 x\right)$