Question

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}}\), then \(\displaystyle \frac{dy}{dx}=\)

• A. \(\frac{\cos x}{1-2y}\)
• B. \(\frac{\sin x}{1-2y}\)
• C. \(\frac{-\sin x}{1-2y}\)
• D. \(\frac{-\cos x}{1-2y}\)

Hint:

For infinite radicals, replace the repeating radical by \(y\). Then square both sides and differentiate implicitly.

Answer 1

The Correct Option is D