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Multivariable chain rule

  1. Jan 2, 2012 #1
    1. The problem statement, all variables and given/known data
    z = f (x^2 + y^2)
    prove using multi var chain rule that

    y * dz/dx - x * dz/dy = 0


    2. Relevant equations



    3. The attempt at a solution

    honestly i just need to no how to start it then im sure i could figure the rest out

    so i would find dz/dx and dz/dy then what would x and y be? and do i substiude any values of x and y to prove it works?
     

    Attached Files:

  2. jcsd
  3. Jan 2, 2012 #2
    z=f(g(x,y)), where g(x,y)=x^2+y^2. Now what does the chain rule tell you about, say ∂z/∂x?
     
  4. Jan 2, 2012 #3
    something like dz/dx = dz/dg dg/dx?

    (d = that stupid partial sign)
     
  5. Jan 2, 2012 #4

    SammyS

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    If you use the "Go Advanced" button below the message box, then you have a new message box with a set of symbols on the right. Find the stupid ' ∂ ' there !
     
  6. Jan 2, 2012 #5

    Dick

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    f is a function of one variable. You could also write ∂z/∂g as f'(g(x,y)). Now what's ∂g/∂x?
     
  7. Jan 2, 2012 #6
    2x * 1?
     
  8. Jan 3, 2012 #7

    ehild

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    Yes.

    ehild
     
  9. Jan 3, 2012 #8
    tys dick and ehild

    think i got it
     
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