# What's the generalisation of the quotient rule for higher derivatives?

I know that the product rule is generalised by Leibniz's general rule and the chain rule by Faà di Bruno's formula, but what about the quotient rule? Is there a generalisation for it analogous to these? Wikipedia mentions both Leibniz's general rule and Faà di Bruno's formula for the product and the chain rule, but rather nothing for the quotient rule.

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that's because you can apply Faa di Bruno's formula to g(x)^{-1} and then the product rule to f(x) and g(x)^{-1}. –  Qiaochu Yuan Sep 24 '10 at 5:00

As others have already said, you just apply the product rule to $f.g^{-1}.$ However, the is an American Mathematical Monthly article on how NOT to do it, which you may find instructive.

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Quotient Rule is actually Product Rule.

$D(u/v) = D(uw)$ where $w = 1/v$.

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