Question

Differentiate the following functions with respect to x:
$x^{3}sinx$

Answer 1

We have,

$\frac{d}{dx}\left(x^{3}sinx\right)$

$=sinx\frac{d\left(x^3\right)}{dx}+x^3\frac{d\left(sinx\right)}{dx}$ [Using product rule]

$=sinx.3x^2+x^3.cosx$

$=x^2(3sinx+xcosx)$