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# Puzzles

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## x to the power of x again

Let $$y=x^{x^{x^{x^{...}}}}$$ [$$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ($$x$$ to the power of ...))) with an infinite number of $$x$$s]. What is $$\frac{dy}{dx}$$?
If you enjoyed this puzzle, check out Sunday Afternoon Maths V,
puzzles about differentiation, or a random puzzle.