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## Main Question or Discussion Point

d(x^^n)/dx = ?

- Thread starter japplepie
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- #1

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d(x^^n)/dx = ?

- #2

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What is (x^^n)?

- #3

Mentallic

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It's tetration which represents a double up arrow in Knuth's up arrow notation. Basically a power tower of x's n high:What is (x^^n)?

[tex]x^{x^{.^{.^{.^x}}}}[/tex]

And I don't see any simple solution to this problem.

- #4

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Im only looking for the formula for integer values of x, will that make it simpler?It's tetration which represents a double up arrow in Knuth's up arrow notation. Basically a power tower of x's n high:

[tex]x^{x^{.^{.^{.^x}}}}[/tex]

And I don't see any simple solution to this problem.

- #5

HallsofIvy

Science Advisor

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That function is not even **defined** for integer values of x.

- #6

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Sorry, what I meant was positive integers.That function is not evendefinedfor integer values of x.

- #7

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- #8

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ok I got it

d(x ^^ n) / dx = x ^^ n * d(x ^^ ( n -1) * ln x ) / dx

Follow up question:

lim i→ ∞ { d^{i}(x ^^ n) / dx^{i} } converge?

d(x ^^ n) / dx = x ^^ n * d(x ^^ ( n -1) * ln x ) / dx

Follow up question:

lim i→ ∞ { d

Last edited:

- #9

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It would be better if you type in latex.ok I got it

d(x ^^ n) / dx = x ^^ n * d(x ^^ ( n -1) * ln x ) / dx

Follow up question:

lim i→ ∞ { d^{i}(x ^^ n) / dx^{i}} converge?