If y = ( cos x2)2 then (dy/dx) is equal to:

Question

If y = ( cos x2)2 then (dy/dx) is equal to: (A) - 4x sin 2x2 (B) - x sin x2 (C) - 2x sin 2x2 (D) - x cos 2x2

Tardigrade Admin · Accepted Answer

As given: y = ( cos x2)2 Diff both side w.r.t 'x' (dy/dx) = 2 cos x2 (- sin x2)2x = - 4 x cos x2 sin x2 = - 2x (2 sin x2 cos x2) (∵ : sin 2 θ = 2 sin θ cos θ) = - 2x sin 2x2

Q. If $y = (cos x^{2})^{2}$ then $\frac{d y}{d x}$ is equal to:

$- 4 x sin 2 x^{2}$

$- x sin x^{2}$

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

$- x cos 2 x^{2}$

As given : $y = (cos x^{2})^{2}$
Diff both side w.r.t 'x'
$\frac{d y}{d x} = 2 cos x^{2} (- sin x^{2}) 2 x$
$= - 4 x cos x^{2} sin x^{2}$
$= - 2 x (2 sin x^{2} cos x^{2})$
$(∵ sin 2 θ = 2 sin θ cos θ)$
$= - 2 x sin 2 x^{2}$

Q. If y=(cosx2)2 then dxdy​ is equal to:

−4xsin2x2

−xsinx2

−2xsin2x2

−xcos2x2