Question

If $y={\cos }^2\frac{3x}{2}-{\sin }^2\frac{3x}{2}$ , then $\frac{d^{2}y}{d{x}^2}$ is

• A. $3\sqrt{1-y^2}$
• B. $9y$
• C. $-3\sqrt{1-y^2}$
• D. $-9y$

Answer 1

The correct option is D $-9y$

$y={\cos }^2\frac{3x}{2}-{\sin }^2\frac{3x}{2}y=\cos (2\times \frac{3x}{2})=\cos 3x$
$\frac{dy}{dx}=-3\sin 3x$
$\frac{d^{2}y}{d{x}^2}=-9\cos 3x=-9y$