If $y=\cos \left(\sin x^2\right)$, then $\frac{d y}{d x} a t x=\sqrt{\frac{\pi}{2}}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & y=\cos \left(\sin x^2ight) \ & \Rightarrow \frac{d y}{d x}=-\sin \left(\sin x^2ight) \cdot \cos x^2 \cdot 2 x \ & \frac{d y}{d x}\left(a t x \sqrt{\frac{\pi}{2}}ight)=-\sin \left(\sin \frac{\pi}{2}ight) \cdot \cos \cdot 2 	imes \sqrt{\frac{\pi}{2}} \ & =-\sin (1) 	imes 0 	imes 2 	imes \sqrt{\frac{\pi}{2}}=0\end{aligned}$

If $y=\cos \left(\sin x^2\right)$, then $\frac{d y}{d x} a t x=\sqrt{\frac{\pi}{2}}$ is

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