Question

The derivative of

\[ y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots \infty}}} \] 

is ______.

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

Hint:

For $y=\sqrt{f(x)+\sqrt{f(x)+\dots}}$, the derivative is always \[ \dfrac{f'(x)}{2y-1} \]

Answer 1

The Correct Option is D