math: f'(x^x)

Discussion in 'Homework Help' started by bug13, Mar 15, 2012.

  1. bug13

    Thread Starter Well-Known Member

    Feb 13, 2012
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    I am stuck with this problem, please explain how to do it, more importantly, why, what concept and what principle is used, thanks

    f'(x^x), the answer is: (x^x)*(1+ln(x))
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    Here is a hint. Take any expression. Then take the natural logarithm of it. Then take the exponential of it. That expression is unchanged. In other words take a funtion y(x). The following is true.

    y(x)=exp(ln(y))

    So, can you find the derivative of exp(ln(x^x))?
     
    bug13 likes this.
  3. bug13

    Thread Starter Well-Known Member

    Feb 13, 2012
    1,208
    38
    your hints is a lot better than WolframAlpha, nice and easy to understand :)

    I solved it now, thanks a lot
     
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