Given a function $$y=\sqrt{log(x)+\sqrt{log(x)+\ldots}}$$ then what is the value of $\frac{dy}{dx}$.
My approach was to assume the inner radical as $y$ and then by equation manipulation we get $y’(2y-1)=\frac{1}{x}$. I am getting the value of $y’$ but how can I prove this is rigorously (because this is an infinite series I have to use real analysis to make it rigorous) .
I am unable to show whether $y$ is convergent or divergent. How to solve this using epsilon delta definition of limits?