At x = sqrt{frac{pi}{2}},find the value of fr | vedclass

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(C) Let $y = \cos(\sin(x^2))$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = -\sin(\sin(x^2)) \cdot \frac{d}{dx}(\sin(x

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(C) Let $y = \cos(\sin(x^2))$.Applying the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = -\sin(\sin(x^2)) \cdot \frac{d}{dx}(\sin(x^2))$$\frac{dy}{dx} = -\sin(\sin(x^2)) \cdot \cos(x^2) \cdot 2x$Now,substitute $x = \sqrt{\frac{\pi}{2}}$ into the derivative:At $x = \sqrt{\frac{\pi}{2}}$,$x^2 = \frac{\pi}{2}$.$\frac{dy}{dx} = -\sin(\sin(\frac{\pi}{2})) \cdot \cos(\frac{\pi}{2}) \cdot 2\sqrt{\frac{\pi}{2}}$Since $\cos(\frac{\pi}{2}) = 0$,the entire expression becomes:$\frac{dy}{dx} = -\sin(1) \cdot 0 \cdot 2\sqrt{\frac{\pi}{2}} = 0$.

At $x = \sqrt{\frac{\pi}{2}}$,find the value of $\frac{d}{dx} \cos(\sin(x^2))$.

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