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Homework Help: Second partial derivative of v=e^(x*e^y)

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the second partial derivative of v=e^(x*e^y)


    2. Relevant equations

    I know that I need to find Vx and Vy first and then the second partial derivative would be Vxx, Vyy, Vxy.

    3. The attempt at a solution

    I'm really confused on how to find Vx or Vy
    Vx= the derivative with regards to x, if y is a constant
    so would it be Vx=e^(x*e^y) * (e^y)?
    Any help would be great
     
  2. jcsd
  3. Oct 27, 2011 #2

    gb7nash

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    You're forgetting one.

    That's correct. What's Vy?
     
  4. Oct 27, 2011 #3
    Would Vy= e^(x*e^y) * (xe^y)
     
  5. Oct 27, 2011 #4

    gb7nash

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    Correct. Now you need to take the second partial derivatives.
     
  6. Oct 27, 2011 #5
    Vxx would be the second derivative with respect to x but keeping y as a constant. This is where I get confused. Would it be:

    Vxx=e^(xye^y)(ye^y)
    = e^(xy^2e^y)
     
  7. Oct 27, 2011 #6
    Wait, you would add the exponents, not multiply them.
    So Vx= e^((xe^y)+y)
    Vxx= e^(xe^y+y) * (e^y)
     
  8. Oct 27, 2011 #7

    gb7nash

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    Correct
     
  9. Oct 27, 2011 #8
    Ok then Vyy= xe^((xe^y)+y) * (x(e^y) +1)

    Then Vxy= e^((xe^y)+y) * ((xe^y)+1) and Vyx is the same as Vxy

    As an aside, how would I integrate t(t-1)^1/2 ?
     
  10. Oct 27, 2011 #9

    gb7nash

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    Correct.

    Try integration by parts.
     
  11. Oct 28, 2011 #10

    SammyS

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    Use the substitution: u = t-1 .
     
  12. Oct 28, 2011 #11

    gb7nash

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    Good call. Both methods should work, but this is much simpler to do.
     
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