Calculate:$y'$ for $y = x^{x^{x^{x^{x^{.^{.^{.^{\infty}}}}}}}}$ and $y = \sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+....\infty}}}}$ (1) If  $y = x^{x^{x^{x^{x^{.^{.^{.^{\infty}}}}}}}}$
(2) If $y = \sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+....\infty}}}}$
then find $y'$ in both cases
(3)If $ y= \sqrt{\tan x+\sqrt{\tan x+\sqrt{\tan x+\sqrt{\tan x+....\infty}}}}\ $ then find$\ (2y-1)\frac{dy}{dx}$

Hint


*

*$$ y = x^y $$

*$$ y^2 = x + y $$


As mentioned in comments, to solve the first one; you might need to take a look at some of the applications of Omega Function.
