Question

If \( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \), then find \( \frac{dy}{dx} \).

• A. \( x + \frac{1}{x} \)
• B. \( \frac{1}{1 + x} \)
• C. \( -\frac{1}{(1 + x)^2} \)
• D. \( \frac{x}{1 + x} \)

Hint:

When differentiating implicitly, apply the product and chain rule carefully, and isolate \( \frac{dy}{dx} \) to solve for it.