Question

If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is equal to:

• A. \( \frac{\sin \sqrt{a}}{\sin(a + y)} \)
• B. \( \frac{\sin^2(a + y)}{a} \)
• C. \( \frac{\sin(a + y)}{a} \)
• D. None of these

Hint:

When differentiating implicit equations, apply the chain rule carefully to find \( \frac{dy}{dx} \).

Answer 1

The Correct Option is C

Differentiate implicitly with respect to \( x \) and solve for \( \frac{dy}{dx} \) using standard differentiation techniques.
Final Answer: \[ \boxed{\frac{\sin(a + y)}{a}} \]