Q102 / 180 · COMEDK 2020 · Mathematics
If $y=\cos ^{2} \frac{3 x}{2}-\sin ^{2} \frac{3 x}{2}$, then $\frac{d^{2} y}{d x^{2}}$ is
- A$9 y$
- B$-3 \sqrt{1-y^{2}}$
- C$3 \sqrt{1-y^{2}}$
- Correct answerD$-9 y$
Solution
We have,
$$
y=\cos ^{2} \frac{3 x}{2}-\sin ^{2} \frac{3 x}{2} \Rightarrow y=\cos 3 x
$$
$\rightarrow \quad \frac{d y}{d x}=-\sin 3 x-3=-3 \sin 3 x$ and $\quad \frac{d^{2} y}{d x^{2}}=-3 \cos 3 x \cdot 3=-9 \cos 3 x=-9 y$
Hence, the correct answer is option: 'D'.