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

• A

  $\frac{2 \cos 5 \theta+\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$
• B

  $\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}$
• Correct answer
  C

  $\frac{2 \cos 5 \theta+\cos 3 \theta \cos 2 \theta}{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}$
• D

  $\frac{2 \cos 5 \theta-\sin 3 \theta \sin 2 \theta}{2 \cos 5 \theta-\cos 3 \theta \cos 2 \theta}$

Hence, the correct answer is option: 'C'.