What is the derivative of (x^2)(e^x)?

Feb 27, 2016

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

Explanation:

Given -

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

Use the product rule to differentiate this.

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