If y=cosx+cosx+⋯+∞, then dydx= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

$y = \sqrt{\cos x + y}$

Squaring on both sides

$y^{2} = \cos x + y$

$2 y . \frac{d y}{d x} = - \sin x + \frac{d y}{d x}$

$(2 y - 1) \frac{d y}{d x} = - \sin x$

$\frac{d y}{d x} = \frac{- \sin x}{2 y - 1}$

$\frac{d y}{d x} = \frac{\sin x}{1 - 2 y}$

If $y = \sqrt{\cos x + \sqrt{\cos x + \dots + \infty}}$ , then $\frac{d y}{d x} =$