Question

If $y={\left(\cos x^2\right)}^2$, then $\frac{dy}{dx}$ is equal to:

• A. $-4x\sin 2x^2$
• B. $-x\sin x^2$
• C. $-2x\sin 2x^2$
• D. $-x\cos 2x^2$

Answer 1

Answer: (C)

As given : $y={\left(\cos x^2\right)}^2$
Diff both side w.r.t '$x$'
$\frac{dy}{dx}=2\cos x^2\left(-\sin x^2\right)2x=-4x\cos x^2\sin x^2$
$=-2x\left(2\sin x^2\cos x^2\right)=-2x\sin 2x^2$