Question

Differentiate the following equation:
$x^3{e}^{x}cosx$

Answer 1

We have,
$\frac{d}{dx}\left(x^3{e}^{x}cosx\right)$
$=e^{x}cosx\frac{d}{dx}\left(x^3\right)+x^{3}cosx\frac{d}{dx}\left(e^x\right)+x^3{e}^x\frac{d}{dx}\left(cosx\right)$ [Using product rule]
$=e^{x}cosx\times 3x^2+x^{3}cosx\times e^x+x^3{e}^x(-sinx)$
$=x^2{e}^x(3cosx+xcosx+x(-sinx\left)\right)$
$=x^2{e}^x(3cosx+xcosx-xsinx)$