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Derivative of Square Root

  1. Mar 22, 2009 #1
    I can't figure out
    Derivative of (sq. rt of x)^x

    Can anyone help me?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 22, 2009 #2

    djeitnstine

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    Gold Member

    Welcome to PF =]

    Use the chain rule, this is simply a function within another function. the outer function just happens to be an exponential. [tex]\frac{d}{dx}f^x=f^x ln(f)[/tex] (if I remember correctly)
     
  4. Mar 22, 2009 #3
    if this is what you mean :

    find f(x) prime, where f(x) = sqrt(x)^x

    Before I help you, you need to help me. Tell me what concept you have learned that could
    apply to this problem
     
  5. Mar 23, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, that's incorrect.
     
  6. Mar 23, 2009 #5
    Here's how I did it.

    [tex]\frac{d}{dx}[/tex](xx/2)

    [tex]\frac{d}{dx}[/tex]e(x/2)ln(x)

    (1/2)(1 + ln(x))e(xln(x))/2

    [tex]\frac{1 + ln(x)}{2}[/tex] * x(x/2)
     
  7. Mar 23, 2009 #6
    looks good to me.
     
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