How do you find the derivative of sqrt(x+sqrt(x+sqrt(x+.......)))?

Answer 1

y = √(x+√(x+√(x+...)))
y^2 = x+√(x+√(x+...)))
y^2 = x+y
2yy' = 1+y'
y' = 1/(2y-1) = 1/[2√(x+√(x+...)))-1]