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Crazy Partial derivative problem

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Let W = F(u(s,t),v(s,t))

    (in my notation, u_s would represent du/ds
    u(1,0) = -7
    v(1,0) = 3
    u_s(1,0)=8
    v_s(1,0)=5
    u_t(1,0)=-2
    v_t(1,0)=-4

    F_u(-7,3)=-8
    F_v(-7,3)=-2

    Find W_s(1,0) and W_v(1,0)

    Sort of having a hard time getting started here... I believe
    W_s = df/du*du/ds + df/dv*dv/ds
    and likewise for W_v...
    I don't know how to make the knowledge of F_u(-7,3)=-8 and F_s(-7,3)=-2 useful though.
     
  2. jcsd
  3. Oct 15, 2013 #2

    arildno

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    F_u=G(u(s,t),v(s,t))
    When (s,t)=(1,0), we must evaluate:
    F_u(u(1,0),s(1,0))
     
  4. Oct 15, 2013 #3
    how do I do that with no actual equations X_x?
     
  5. Oct 15, 2013 #4

    arildno

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    You have all the quantities you need calculate W_s.

    To get you started
    F_u(u(1,0),v(1,0))=F_u(-7,3)=-8
    u_s(1,0)=8

    so F_u*u_s=-8*8=64

    And so on.
     
  6. Oct 15, 2013 #5
    it doesn't matter that the coordinates change from (-7,3) to (1,0)?? I confused X_x
     
  7. Oct 16, 2013 #6

    arildno

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    (1,0) are (s,t)-coordinates, whereas (-7,3) are the corresponding (u,v)-coordinates.
     
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