If `y=(sqrt(x))^(sqrt(x))^(((sqrt(x))dotoo))` , show that `(dy)/(dx)=(y^2)/(x(2-ylogx))` .

Explanation

To solve the problem, we need to show that if \( y = (\sqrt{x})^{(\sqrt{x})^{(\sqrt{x})^{\cdots}}} \), then \( \frac{dy}{dx} = \frac{y^2}{x(2 - y \log x)} \).

### Step-by-Step Solution:

1. **Define the equation**:
We start with the equation given in the problem:
\[
y = (\sqrt{x})^y
...