1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    Correct.

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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

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

    gb7nash

    User Avatar
    Homework Helper

    Good call. Both methods should work, but this is much simpler to do.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second partial derivative of v=e^(x*e^y)
Loading...