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How can i differentiate this ?

  1. May 4, 2005 #1
    I wonder if this can be differentiated ,if it can then what is the derivative of
    [x^x^x^x^x^x.....]^[(x^2)^(x^2)^(x^2).....]^[(x^3)^(x^3)^(x^3).....]^[(x^4)^(x^5)...]......................
    thank you
     
  2. jcsd
  3. May 4, 2005 #2
    what do all the dots mean? What order do you want the exponentiation in (it's not associative)?
     
  4. May 4, 2005 #3

    dextercioby

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    From left to right i guess.I assume it resembles power tower.


    Daniel.
     
  5. May 4, 2005 #4

    saltydog

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    The power tower:

    [tex]y(x)=x^{x^{x^. . .}}}[/tex]

    is defined for:

    [tex]e^{-e}\leq x\leq e^{1/e}[/tex]

    Note that the upper limit for a power tower is about 1.44467. However above, you're using "2" and larger values, you know [itex]x^2[/itex] and more. Thus I claim the expression is 0 for x<1, 1 for x=1, and infinity for x>1. It's derivative therefore is zero for [itex]0\leq x\leq 1[/itex] and undefined for x>1.

    However, I've just started looking at it and wouldn't bet more than a dollar.
     
  6. May 9, 2005 #5
    Here's a better question - "Can you draw the graph of it ?"

    If you cannot draw a graph of that thing, then chances are pretty good that you cant differentiate it either.
     
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