Question

Find the differential coefficient of the function $x^2$ log x $\sin$ x with respect to x.

Answer 1

We need to find the differential coefficient of the function $x^{2}logxsinx$ with respect to $x$.

Let $y=x^{2}logxsinx$

We need to find $\frac{dy}{dx}$.

Consider $y=x^{2}logxsinx$

$\frac{dy}{dx}=\frac{d}{dx}\left(x^2\right)logxsinx+x^2\frac{d}{dx}\left(logxsinx\right)$

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

$=2x\left(logxsinx\right)+x^2[\frac{sinx}{x}+\log xcosx]$

$\frac{dy}{dx}=2x\left(logxsinx\right)+xsinx+x^{2}logxcosx$