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First year uni math problem

  1. May 18, 2009 #1
    first year uni math problem~~

      if w=f(u,v)has continuous partial derivatives and u=x+y
      and v=x-y,use the chain rule to show that
      
      (dw/dx)/(dw/dy)=(df/du)^2-(df/dv)^2


    this is a first year uni math problem,is there anyone can help we with it??
    thx a lot! :cry:
     
  2. jcsd
  3. May 18, 2009 #2
    Re: first year uni math problem~~

    do you know the chain rule?
     
  4. May 18, 2009 #3
    Re: first year uni math problem~~

    yeah i know,but no idea hw do i apply on this question~~
     
  5. May 18, 2009 #4
    Re: first year uni math problem~~

    [tex] \frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x}[/tex]

    [tex] \frac{\partial w}{\partial y} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial y} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial y}[/tex]
     
  6. May 18, 2009 #5
    Re: first year uni math problem~~

    ok,i got it,but i still not clear which varible i take respect to when i differenciate for u=x+y and v=x-y....
     
  7. May 18, 2009 #6
    Re: first year uni math problem~~

    [tex] \frac{\partial w}{\partial x} = \frac{\partial f}{\partial u} \frac{\partial u}{\partial x} + \frac{\partial f}{\partial v} \frac{\partial v}{\partial x} = \frac{\partial f}{\partial u}*1 + \frac{\partial f}{\partial v}*1 = \frac{\partial f}{\partial u} + \frac{\partial f}{\partial v}[/tex]
     
  8. May 18, 2009 #7
    Re: first year uni math problem~~

    oh!!!!i got it~~~ thx mates~
     
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