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Perfect Differential.

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi, I have an exam tomorrow and I'm trying to do the following question which I've almost solved:

    Find the perfect differential of the following:

    [(x² + 2xy) / (x + y)² ]dx - [x² / (x + y)² ]dy

    I differentiated the first term with respect to 'y' and then the second term with respect to x, equated them but they werent the same, what could I be doing wrong?

    The problem is I can't seem to get both terms to equal eachother unless i cancel the denominator..but why cant i get them to equal eachother if i differentiate with the denominators too? Should be the same...?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 17, 2009 #2

    quasar987

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    I get that they are not equal either.
     
  4. May 17, 2009 #3
    If I were to cancel the denominator and then differentiate they actually equal eachother. I'm guessing this question was meant to trick me into cancelling it then?
     
  5. May 17, 2009 #4

    quasar987

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    I don't think so. Go see your prof about this.
     
  6. May 18, 2009 #5

    HallsofIvy

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    What does "Find the perfect differential of the following" mean?

    I know what determining whether a differential is a perfect differential or not means but this seems to imply that there is some perfect differential associated with this differential. My first guess my be to change it in someway so that this becomes a perfect differential- for example, multiplying the entire expression by [itex](x+ y)^2[/itex] makes it a perfect differential- but that is certainly not unique so "the" perfect differential would not apply.
     
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