Question

Differentiation of $x\sin x$ with respect to $x$ is

• A. $x\cos x+\sin x$
• B. $x\sin x+\cos x$
• C. $x\cos x$
• D. $x\cos x-\sin x$

Answer 1

The correct option is A $x\cos x+\sin x$

Given, $y=x\sin x$

$\therefore \frac{d}{dx}\left(x\sin x\right)=x\frac{d}{dx}\left(\sin x\right)+\sin x.\frac{d}{dx}\left(x\right)$

$=x\cos x+\sin x\left(1\right)$

$=x\cos x+\sin x$