Question

If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals

• A. \( \frac{\sec^3 \theta}{a \theta} \)
• B. \( \frac{\sec^2 \theta}{a} \)
• C. \( a \theta \cos^3 \theta \)
• D. \( \frac{\sec^2 \theta}{a\theta} \)

Hint:

To compute higher-order derivatives in parametric equations, use the chain rule along with parametric differentiation.