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Multivariable chain rule

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

    Let f be a differentiable function of one variable, and let
    z = f(x + 2y). Show that
    2∂z/∂x − ∂z/∂y = 0

    2. Relevant equations

    Multi-variable chain rule

    3. The attempt at a solution

    I have no idea where to start with this, any advice would be greatly appreciated.

    Thanks in advance,
    Doug
     
  2. jcsd
  3. Jan 1, 2012 #2

    Dick

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    z=f(g(x,y)), where g(x,y)=x+2y. Now what does the chain rule tell you about, say ∂z/∂x?
     
  4. Jan 1, 2012 #3
    would it be f'(g(x,y))*1?
     
  5. Jan 1, 2012 #4

    Dick

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    Yes! Now do ∂z/∂y.
     
  6. Jan 1, 2012 #5
    f'(g(x,y)))*2
     
  7. Jan 1, 2012 #6

    Dick

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    So 2∂z/∂x − ∂z/∂y equals what?
     
  8. Jan 1, 2012 #7
    0! Thanks for the help.

    Doug.
     
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