Talk:Quotient rule

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1 Informal proof
2 Total differential proof
3 Fix needed in a proof
4 From the product rule

[edit] Informal proof

Out of curiosity, what exactly is there about the informal proof that makes it informal? Cburnett 23:22, 3 Feb 2005 (UTC)

I guess it's considered an informal proof because it's based off the product rule, while the "formal" proof is based off the difference quotient, which is more direct. I changed the headings to be more specific. - Evil saltine 05:11, 4 Feb 2005 (UTC)

The proof is informal because it contains a hidden assumption, that the derivative of f exists. David Radcliffe 02:44, 26 May 2007 (UTC)

[edit] Total differential proof

The total differential proof uses the fact that the derivative of 1/x is −1/x². But without the quotient rule, one doesn't know the derivative of 1/x, without doing it directly, and once you add that to the proof, it doesn't seem as "elegant" anymore, but without it, it seems circular. Revolver 16:03, 30 September 2005 (UTC)

I would vote to remove that proof altogether. Too many proofs in this article, and they are lengthy and using lots of calculations. Oleg Alexandrov 17:44, 2 October 2005 (UTC); I guess I'll go ahead and get rid of it. I'll save the section incase anyone wants it back. (Frazz 18:04, 7 February 2007 (UTC))
On second thought, it's fine really. (Frazz 16: 30, 8 February 2007 (UTC))

[edit] Fix needed in a proof

A proof of the quotient rule is not complete. Why $h (x)$ ≠ 0 does implies $h(x+\Delta x)\ne 0$ ? I have seen a proof of the quotient rule based on a characterization theorem (don't know its proper English name). --Matikkapoika 01:25, 15 November 2006 (UTC)