If y = cos^{2}left(frac{5x}{2}right) - sin^{2 | vedclass

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(D) We are given the function $y = \cos^{2}\left(\frac{5x}{2}ight) - \sin^{2}\left(\frac{5x}{2}ight)$.Using the trigonometric identity $\cos(2	he

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$-25 y$

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(D) We are given the function $y = \cos^{2}\left(\frac{5x}{2}ight) - \sin^{2}\left(\frac{5x}{2}ight)$.Using the trigonometric identity $\cos(2	heta) = \cos^{2}(	heta) - \sin^{2}(	heta)$,we can simplify the expression by setting $	heta = \frac{5x}{2}$.Thus,$y = \cos\left(2 	imes \frac{5x}{2}ight) = \cos(5x)$.Now,we find the first derivative with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(\cos(5x)) = -5 \sin(5x)$.Next,we find the second derivative with respect to $x$:$\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(-5 \sin(5x)) = -5 	imes 5 \cos(5x) = -25 \cos(5x)$.Since $y = \cos(5x)$,we substitute $y$ back into the expression:$\frac{d^{2}y}{dx^{2}} = -25y$.

If $y = \cos^{2}\left(\frac{5x}{2}\right) - \sin^{2}\left(\frac{5x}{2}\right)$,then $\frac{d^{2}y}{dx^{2}} = $

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