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Exponential/Logarithmic functions

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of
    y = sqrt(XX)



    3. The attempt at a solution

    I tried using the equation d/dx (ax) = ax * ln a

    Is this even a right start? The square root kind of throws me off. I'm not sure if this is the right equation to use or not. I was told the answer was

    Xx / (2*sqrt(Xx)) but i'm not even sure how to get there given the answer. any hints or help? :(
     
  2. jcsd
  3. Sep 14, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    x=e^log(x). So x^x=e^(log(x)*x). Try treating it that way. Your given equation is only valid for 'a' being a constant. You can handle the sqrt by either using the chain rule or just the rules of exponents. sqrt(x^x)=(x^x)^(1/2)=x^(x/2), right?
     
  4. Sep 14, 2011 #3

    lanedance

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    how about starting by writing as
    [tex] y = \sqrt{x^x} = (x^x)^{\frac{1}{2}} [/tex]

    then simplify and consider taking the log of both sides and implicit differentiation
     
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