Question

Derivative of $f\left(x\right)=x^2\sin x$ is

• A. $2x\sin x+x^2\cos x$
• B. $2x\sin x+x\cos x$
• C. $x\sin x+x^2\cos x$
• D. $2x\sin x-x^2\cos x$

Answer 1

The correct option is A $2x\sin x+x^2\cos x$

Given, $f\left(x\right)=x^2\sin x$
So, the derivative of the function is given as
$\frac{df\left(x\right)}{dx}=\frac{d\left(x^2\sin x\right)}{dx}$
Using product rule we have
$\sin x\frac{d{x}^2}{dx}+x^2\frac{d\sin x}{dx}=2x\sin x+x^2\cos x$