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Taking differentials

  1. Nov 27, 2005 #1
    Hi,
    I'm trying to take differentials of the following equation

    [tex](p + \frac{a}{{V^2 }})(V - b) = C[/tex]

    in order to find the partial derivative [tex]\frac{{\partial p}}{{\partial V}}[/tex]

    I know there's an easier way to do it but I have to take differentials.
    I'm just not sure how to deal with the brackets without multiplying out (I can't rearrange the equation).

    Any hints welcome.
     
  2. jcsd
  3. Nov 27, 2005 #2

    HallsofIvy

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    Use the product rule!
     
  4. Nov 27, 2005 #3
    How do I do that with differentials?
    I end up with crazy results.
     
  5. Nov 27, 2005 #4

    Physics Monkey

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    You "can't" rearrange the equation, as in the problem won't let you? The product rule for differentials is [tex] d(fg) = g df + f dg [/tex].
     
  6. Nov 27, 2005 #5
    If I use that product rule I end up with a free floating [tex]p[/tex] in my equation where I know that [tex]\frac{{\partial p}}{{\partial V}}[/tex] doesn't have a term in [tex]p[/tex]
     
  7. Nov 27, 2005 #6

    Physics Monkey

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    Yes, you then have to solve for p in terms of V using the original equation. This I why I don't undestand why you can't just solve for p in terms of V from the start since you have do it eventually anyway.
     
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