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    This is just for fun...to see if i can do it...

    I'm trying to differentiate e^x^x^x

    Let y = e^x^x^x

    y = [(e^x)^x]^x

    THe Chain Rule states dy/dx = dy/du * du/dx

    Let u = e^x^x

    ==> y = u^x

    dy/du = xu^(x-1)


    u = (e^x)^x

    Let a = e^x

    Therefore u = a^x

    du/dx = xa^x-1

    = x(e^x)^x-1

    dy/dx = dy/du * du/dx

    = xu^(x-1) * x(e^x)^(x-1)

    Now I'm stuck. I think ive gone wrong and I cant do the multiplication. Please help!!

    Thanks in advance

    you are an odd person. I would do it, but the prospect's highly daunting.

    Note that the expression e^x^x^x is ambiguous (is it e^(x^x^x) or (e^x^x)^x?) and the convention is to treat it as e^(x^x^x) which is different from what you're doing.

    The reason for this convention is that (a^b)^c is just a^(bc). Apply this several times and you'll see ((e^x)^x)^x actually simplifies quite nicely.
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Updated: January 19, 2010

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