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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
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 equal to
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Answer

$\text { (c) : Given, } y=\cos ^2\left(\frac{3 x}{2}\right)-\sin ^2\left(\frac{3 x}{2}\right)$
$\Rightarrow y=\cos 3 x \Rightarrow \frac{d y}{d x}=-3 \sin 3 x$
$\Rightarrow \frac{d^2 y}{d x^2}=-3 \times 3 \cos 3 x=-9 \cos 3 x=-9 y$

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