Talk:Logarithmic derivative

Use in elementary calculus

Should this not be mentioned? Every calculus text I've ever read (e.g. Stewart's) teaches students logarithmic differentiation as a method to take derivatives of complicated products (since this converts them into sums, which one can differentiate term by term). I don't have time right now to do this, but does anyone else think there could be more here (along the lines of chain rule or implicit function#Implicit differentiation? --Cheeser1 10:41, 17 October 2007 (UTC)

I got here from the redirect from "Logarithmic differentiation". It's not immediately obvious that logarithmic differentiation (as presented in Stewart) has anything to do with the description given here (additionally obscured by the notational difference between Stewart's ${\frac {1}{y}}{\frac {dy}{dx}}$ and this article's ${\frac {f'}{f}}$). I think some words to connect the concrete technique with this article's description-of-properties would be good. What I was originally looking for was the conditions (if any) under which the procedure of logarithmic differentiation of $f(x)=...x...$ yields a function which is defined, but is not the derivative of $f$, for $x\leq 0$. --216.171.188.181 (talk) 18:37, 18 February 2009 (UTC)

This is a slick trick! But I'm not sure how useful it is. Anyway, I've added it to the article.

I don't think it can give you a wrong solution. If you expand out the formula that you get for f' with this technique (the second displayed formula in my addition) using the definition f = uv, then you recover exactly the usual Leibniz rule. So the only thing that could be different is that the formula coming from the logarithmic derivative might divide by zero somewhere: It might go wrong if f, u, or v have a zero; or equivalently, if u or v has a zero. But the way it goes wrong is by being undefined, not by giving you a wrong answer. So you get at most as much information from this technique as you do from the usual one, and sometimes you get less. If the functions involved are analytic, then you can always analytically continue, and after that you get exactly the usual product. Ozob (talk) 02:08, 19 February 2009 (UTC)

Introduction

I don't get the meaning of "the negative inverse of". Can this be explained, or the words linked to relevant articles? —DIV (128.250.80.15 (talk) 03:14, 24 April 2008 (UTC))

I've never heard of this either, and negative inverse is not a wikipedia article, nor does the first page of a Google (with quotes) bring up anything sensible. I'm going to remove it from the article. If someone wants to put it back, please at least define the term and cite a source, and preferably create the wikipedia article for it too. Quietbritishjim (talk) 11:53, 22 June 2008 (UTC)

Looking over the version history, it appears that this was delivered with several (deliberately?) inaccurate changes at 03:44, 16 February 2008 by User:BadgerPie. The two edits since have just been to patchily revert them, so I'll revert everything back to the version before (then put back the change from \ln to \log that User:LouisWins made since). I'll also give the maths a check over Quietbritishjim (talk) 12:08, 22 June 2008 (UTC)