Question

Differentiate with respect to $x$ : $x^2\cos x$

• A. $2x\cos x-x^2\sin x$
• B. $2x\cos x$
• C. $2x\cos x-x^2$
• D. None of these

Answer 1

Answer: (A)

$2x\cos x-x^2\sin x$

Let $y=x^2\cos x$

Differentiate it with respect to $x$ using by parts $\frac{d\left(uv\right)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}$

so, $\frac{dy}{dx}=x^2(-\sin x)+\cos x\left(2x\right)$

$\frac{dy}{dx}=2x\cos x-x^2\sin x$