Question

Differentiate the following functions with respect to x:
$x^{2}sinxlogx$

Answer 1

We have,

$\frac{d}{dx}\left(x^{2}sinxlogx\right)$

$=sinxlogx\frac{d}{dx}\left(x^2\right)+x^{2}logx\frac{d}{dx}\left(sinx\right)+x^{2}sinx\frac{d}{dx}\left(logx\right)$ [Using product rule]

$=sinxlogx\times 2x+x^{2}logx\times cosx+x^{2}sinx\times \frac{1}{x}$

$=2x\times sinx\times logx+x^2\times cosx\times logx+xsinx$