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Math Help - quotient rule for higher order derivatives

  1. #1
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    quotient rule for higher order derivatives

    what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .
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  2. #2
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    Quote Originally Posted by mmzaj View Post
    what is quotient rule for higher order derivatives ? i mean the one analogous to leibniz rule .
    If you consider that:

     \frac{d}{dx} \bigg(\frac{f(x)}{g(x)}\bigg) = \frac{d}{dx} \bigg(f(x) \times \frac{1}{g(x)}\bigg) = \frac{d}{dx}\bigg( f(x) \times h(x)\bigg) where  h(x) = \frac{1}{g(x)} , then the generalised product rule holds.

    The quotient rule is simply a by-product of the product rule, and one of the most familiar proofs of the quotient rule is based entirely on the product rule.
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  3. #3
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    but then you gotta use the reciprocal rule for the nth derivative , with isn't easier from finding a generalization for the quotient rule !!
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