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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
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
  • A
    $9 y$
  • B
    $-3 \sqrt{1-y^2}$
  • ✓
    $-9 y$
  • D
    $3 \sqrt{1-y^2}$
✓

Answer

Correct option: C.
$-9 y$
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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