Question

If $y=x^{2}sinx,then\frac{dy}{dx}$ will be

• A. $x^{2}cosx+2xsinx$
• B. $2xsinx$
• C. $x^{2}cosx$
• D. $2xcosx$

Answer 1

The correct option is A $x^{2}cosx+2xsinx$

Given

$y=x^2\sin x$

Using

$\frac{d(u.v)}{dx}=v\frac{du}{dx}+u\frac{dv}{dx}$

Differentiating on both sides

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

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

$⟹\frac{dy}{dx}=2x\sin x+x^2\cos x$