Question

The derivative of $\left(x^{2}+1\right) \cos x$ is

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

Answer 1

Answer: (D)

Let $y =\left( x ^{2}+1\right) \cos x$,
Differentiating y w.r.t. x, we get
$\frac{d y}{d x}=\left(x^{2}+1\right) \frac{d}{d x}(\cos x)+\cos x \frac{d}{d x}\left(x^{2}+1\right)$
(by product rule)
$=\left( x ^{2}+1\right)(-\sin x )+\cos x (2 x )$
$=-x^{2} \sin x-\sin x+2 x \cos x$