# How do you differentiate f(x)=2x^2*e^x*sinx using the product rule?

May 4, 2018

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

#### Explanation:

$f ' \left(x\right) = \left(2 {x}^{2} {e}^{x} \sin x\right) '$ $=$

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

$4 x {e}^{x} \sin x + 2 {x}^{2} {e}^{x} \sin x + 2 {x}^{2} {e}^{x} \cos x$ $=$

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