Question

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

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

Answer 1

Answer: (C)

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