# 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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