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If $y=\left(\cos x^{2}\right)^{2}$, then $\frac{d y}{d x}$ is equal to
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Verified Answer
The correct answer is:
$-2 x \sin 2 x^{2}$
$y=\left(\cos x^{2}\right)^{2}$
On differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{d y}{d x} &=2 \cos x^{2} \frac{d}{d x}\left(\cos x^{2}\right) \\
&=2 \cos x^{2} \times\left(-\sin x^{2}\right) \frac{d}{d x}\left(x^{2}\right) \\
&=-4 x \cos x^{2} \sin x^{2} \\
&=-2 x \sin 2 x^{2}
\end{aligned}$
On differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{d y}{d x} &=2 \cos x^{2} \frac{d}{d x}\left(\cos x^{2}\right) \\
&=2 \cos x^{2} \times\left(-\sin x^{2}\right) \frac{d}{d x}\left(x^{2}\right) \\
&=-4 x \cos x^{2} \sin x^{2} \\
&=-2 x \sin 2 x^{2}
\end{aligned}$
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