More fun with power towers, Part 2

Calculus Level 4

\[\huge f(x)=x^{x^{x^{\cdot^{\cdot^\cdot}}}}\]

Let \(f(x) \) defined as the infinite power tower above, defined on the interval \([1,e^{1/e}]\). Find the integer part of the derivative \(f'(\sqrt{2})\).


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