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  4. If y= cos 2((3 x/2))- sin 2((3 x/2)) then (d2 y/d x2) is

Q. If $y=\cos ^{2}\left(\frac{3 x}{2}\right)-\sin ^{2}\left(\frac{3 x}{2}\right)$ then $\frac{d^{2} y}{d x^{2}}$ is

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Solution:

If $y =\cos ^{2}\left(\frac{3 x}{2}\right)-\sin ^{2}\left(\frac{3 x}{2}\right)$
$y=\cos 2\left(\frac{3 x}{2}\right)=\cos 3 x$
$\frac{d y}{d x}=-\sin 3 x \cdot 3$
$\frac{d^{2} y}{d x^{2}}=-3 \cos 3 x \cdot 3=-9 y$

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