The derivative of (x2+1) cos x is

Question

The derivative of (x2+1) cos x is (A) -x2 sin x- sin x-2 x cos x (B) -x2 sin x- sin x+2 cos x (C) -x2 sin x-x sin x+2 cos x (D) -x2 sin x- sin x+2 x cos x

Tardigrade Admin · Accepted Answer

Let y =( x 2+1) cos x, Differentiating y w.r.t. x, we get (d y/d x)=(x2+1) (d/d x)( cos x)+ cos x (d/d x)(x2+1) (by product rule) =( x 2+1)(- sin x )+ cos x (2 x ) =-x2 sin x- sin x+2 x cos x

Q. The derivative of $(x^{2} + 1) cos x$ is

$- x^{2} sin x - sin x - 2 x cos x$

$- x^{2} sin x - sin x + 2 cos x$

$- x^{2} sin x - x sin x + 2 cos x$

$- x^{2} sin x - sin x + 2 x cos x$

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

Q. The derivative of (x2+1)cosx is

−x2sinx−sinx−2xcosx

−x2sinx−sinx+2cosx

−x2sinx−xsinx+2cosx

−x2sinx−sinx+2xcosx