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Query regarding implicit differentiation

  1. Aug 22, 2008 #1
    1. The problem statement, all variables and given/known data

    Use implicit diff to find partial x and partial y if

    x² + y² + z² = 3xyz


    3. The attempt at a solution

    firstly with partial x...

    2x + 2z(∂z/∂x) = 3yz + 3xy(∂z/dx)
    2x - 3yz = 3xy(∂z/dx) - 2z(∂z/∂x)
    2x - 3yz = (3xy - 2z)(∂z/dx)
    (2x - 3yz)/(3xy - 2z) = (∂z/dx)

    yet in the solutions, they have moved all the (∂z/dx) terms to the left hand side thus giving

    (∂z/dx) = (3yz - 2x)/(2z - 3xy)

    Quite obviously this is not the same as my answer. My question is why should the two answers differ? MUST you take all (∂z/dx) terms to the left hand side as some sort of convention?
     
  2. jcsd
  3. Aug 22, 2008 #2

    tiny-tim

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    Homework Helper

    Hi t_n_p! :smile:

    They are the same!

    Yours just has the top and bottom both multiplied by -1. :smile:
    erm … yes!!

    (unless you're writing in Hebrew or Arabic :rolleyes:)

    … you won't lose any marks for not doing it … but if you're asked an ordinary English question "what is an apple?" or "what is ∂z/∂x?", you start the answer with "an apple is …" or "∂z/∂x is …"

    So ∂z/∂x goes on the left! :smile:

    A math proof should sound like good English when you read it out! :wink:
     
  4. Aug 22, 2008 #3
    hmmm, the thought never occured to me...

    also regarding the second point, I meant during the taking the dy/dx and non dy/dx terms to the left or rhs. obviously I would write the answer as dy/dx = .....

    Just having one of those mindblocks...
    Cheers
     
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