If `y=(sqrt(x))^sqrt(x)^sqrt(x)^(dot)^(((oo))),s howt h a t(dy)/(dx)=(y^2)/(x(2-ylogx)`

Explanation

To solve the problem step by step, we need to differentiate the given function and show that \(\frac{dy}{dx} = \frac{y^2}{x(2 - y \log x)}\).

### Step 1: Define the function
We start with the function:
\[ y = (\sqrt{x})^{\sqrt{x}^{\sqrt{x}^{\cdots}}} \]
This expression suggests a recursive definition. We can denote:
...