Question

If $y=x^2\sin \left(x\right)$, then $\frac{dy}{dx}$ will be

• A. $x^2\cos \left(x\right)+2x\sin \left(x\right)$
• B. $2x\sin \left(x\right)$
• C. $x^2\cos \left(x\right)$
• D. $2x\cos \left(x\right)$

Answer 1

The correct option is A $x^2\cos \left(x\right)+2x\sin \left(x\right)$

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