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Partial derivative chain rule proof

  1. Nov 11, 2012 #1
    1. The problem statement, all variables and given/known data

    If u=f(x,y) where x=escost and y=essint

    show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2

    2. Relevant equations

    http://s11.postimage.org/sjwt1wkvl/Untitled.jpg

    3. The attempt at a solution

    ok i don't understand how they got to that


    i don't know what d/ds is supposed to do exactly, i thought it was the second partial derivative of s, but it seems that it's not if we check the answer.


    i basically got e^s cost (d^2/dx^2) + e^s sint (d^2u/dy^2), but they got 6 terms. i am kinda lost, can you explain to me what d/ds is supposed to do?
     
  2. jcsd
  3. Nov 11, 2012 #2
    Maybe you should try typing the problem a little clearer. I think I could help you with this.
     
  4. Nov 11, 2012 #3
    http://s10.postimage.org/fksqxnn3r/image.jpg

    i got 6 terms, but the results are not the same for some reason and i am stuck. it has been like 2 hours and it has been really frustrating
     
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