If y = (cos x^2)^2,then frac{dy}{dx} is equal | vedclass

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Question

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

Vedclass · Accepted Answer

$-2x \sin 2x^2$

Vedclass · Answer

(C) Given $y = (\cos x^2)^2$. Applying the chain rule,we differentiate with respect to $x$: $\frac{dy}{dx} = 2(\cos x^2) \cdot \frac{d}{dx}(\cos x^2)$ $\frac{dy}{dx} = 2(\cos x^2) \cdot (-\sin x^2) \cdot \frac{d}{dx}(x^2)$ $\frac{dy}{dx} = 2(\cos x^2) \cdot (-\sin x^2) \cdot (2x)$ $\frac{dy}{dx} = -4x \sin x^2 \cos x^2$ Using the trigonometric identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$,we have: $\frac{dy}{dx} = -2x(2 \sin x^2 \cos x^2) = -2x \sin 2x^2$.

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

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