Question

If y=√sinx+√sinx+√sinx+......... infinity
show that dy/dx=cosx/2y-1​

Answer 1

Step-by-step explanation:

We have,

$y = \sqrt{ \sin(x) + \sqrt{ \sin(x) + \sqrt{ \sin(x) + ...... \infty } } }$

${y}^{2} = \sin(x) + y$

Differentiating both sides, we get,

$2y \: \frac{dy}{dx} = \cos(x) + \frac{dy}{dx}$

$= > \frac{dy}{dx} = \frac{ \cos(x) }{(2y - 1)}$