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Posted by on Tuesday, October 11, 2011 at 6:50pm.

Please help me find the derivative of f(x) = x^(2^x)

I got to ln(f(x)) = 2^x(lnx) but now I'm stuck..

  • calculus - , Tuesday, October 11, 2011 at 7:31pm

    a good start
    I would change f(x) to y for easier typing

    lny = (2^x)(lnx) , you had that
    now use the product rule on the right side
    y'/y = (2^x)(1/x) + (lnx)(ln2((2^x)
    y' = y( (2^x)/x + ln2(lnx)(2^x))
    = x^(2^x)) [ (2^x)/x + ln2(lnx)(2^x) ]

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