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Is there a way to prove the quotient rule using differentials

  1. Jun 9, 2010 #1
    Specifically, how do you prove the quotient rule using a similar method that Leibniz used for the product rule?: http://en.wikipedia.org/wiki/Product_rule#Discovery_by_Leibniz

    I've tried it once for d(u/v) but I keep getting a vdv term in the denominator.
  2. jcsd
  3. Jun 9, 2010 #2


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    y= u/v

    when you have

    [tex]\Delta y = \frac{v \Deltau - u \Deltav}{v^2 +v \Delta v}[/tex]

    [tex]\frac{\Delta y}{\Delta x} = \frac{v \frac{\Delta u}{\Delta x} - u \frac{\Delta v}{\Delta x}}{v^2 +v \Delta v}[/tex]

    as Δx→ 0, Δv→ 0
  4. Jun 9, 2010 #3
    d'oh, didn't think about vdv as dv approaches zero

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