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Calc Midterm, First Year University (derivative related stuff)

  1. Nov 14, 2008 #1
    1. The problem statement, all variables and given/known data
    If f(x)=x^x for x>0, find the constant a such that f'(a)=2f(a)

    2. Relevant equations

    3. The attempt at a solution



  2. jcsd
  3. Nov 14, 2008 #2
    If f(x) = x^x, then f'(x) =/= x*x^(x-1). That rule works if your exponent is a number, not a function. Rewrite x^x in exponential form and then differentiate using the chain rule to find f'(x).
  4. Nov 15, 2008 #3


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    Science Advisor

    No that is not right. You cannot treat a (x) as a variable in one case (the base) and a constant in the other (the exponent).

    If y= xx then ln(y)= x ln(x). Use the chain rule to find dy/dx.
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