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Homework Help: Derivative of x^(2x)

  1. Aug 4, 2010 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    I only know that it is solved with ln. Something like lnx2x...
     
  2. jcsd
  3. Aug 4, 2010 #2

    Dick

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    x^(2x)=e^(ln(x)*(2x)). Use the chain rule.
     
  4. Aug 5, 2010 #3
    I got:

    (lnx 2x)'=1/x2x+lnx*2=x+2ln x

    e^x+2lnx
    =ex+e2elnx

    ?
     
  5. Aug 5, 2010 #4

    Dick

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    Well, the derivative of 2*x*ln(x) isn't x+2*ln(x). You might want to work on that for a start.
     
  6. Aug 5, 2010 #5
    I am sorry, that was a typo.
    I meant
    2+2lnx NOT x+2lnx
     
  7. Aug 6, 2010 #6

    Dick

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    That's better. Now work on the rest of it. The chain rule says (e^f(x))'=(e^f(x))*f'(x) doesn't it? Put f(x)=ln(x)*(2x).
     
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