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General Form

  1. Apr 5, 2009 #1
    Hello,

    Is there a general form for the nth derivative for a fraction?

    Thanks in advance.
     
  2. jcsd
  3. Apr 6, 2009 #2

    tiny-tim

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    Hello saeddawoud! :smile:

    General form for a product:

    (fg)(n) = f(n)g + nC1f(n-1)g(1) + … + fg(n)

    so the form for f(1/g) is … ? :wink:
     
  4. Apr 8, 2009 #3
    Thank you, it is really helpful, but how to determine the coefficients of each term in general form?

    Regards
     
  5. Apr 8, 2009 #4

    Mute

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    The coefficients are just the binomial coefficients. That's what the nC1 in Tiny Tim's expression is. Written in summation notation:

    [tex](fg)^{(n)} = \sum_{k=0}^{n}\frac{n!}{k!(n-k)!}f^{(n-k)}g^{(k)}[/tex]
     
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