Talk:List of derivatives and integrals in alternative calculi

Lists Low‑importance

	This article is within the scope of WikiProject Lists, an attempt to structure and organize all list pages on Wikipedia. If you wish to help, please visit the project page, where you can join the project and/or contribute to the discussion.ListsWikipedia:WikiProject ListsTemplate:WikiProject ListsList articles
Low	This article has been rated as Low-importance on the project's importance scale.

Mathematics

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
???	This article has not yet received a rating on the project's priority scale.

Based on what is now in the article's table, I think the "multiplicative" derivative and integrals are . . .[edit]

. . . are things I recognize from a high school project of mine in 1963. (These have without a doubt been rediscovered both before and after that.) One approach is to take the usual definitions of derivative and integral and replace addition with multiplication, and multiplication with exponentiation.

For the multiplicative derivative, instead of the limit as h → 0 of (f(x + h) - f(x)) / h one may take instead the limit of (f(x+h) / f(x))^1/h. The multiplicative integral is the inverse operator of the multiplicative derivative.

One may show that under suitable conditions, these multiplicative derivative and integral operators are the same as conjugating the ordinary operators with the exponential function. The multiplicative integral, at least, has an application in the field of survival statistics.

An amusing corollary is that the definite multiplicative integral may be used to calculate the geometric mean of a function over an interval. For example, the geometric mean [of the function f(x) = x over the interval [a,b] where 0 < a < b] is equal to (1/e)(b^b/a^a)^1/(b-a), and so in particular the limiting case of the geometric mean of the numbers in the unit interval (0,1] is 1/e.Daqu (talk) 07:35, 11 March 2010 (UTC)[reply]

Er, um, I just discovered there is an entire article Multiplicative calculus that seems to explain some of these things fairly well.Daqu (talk) 08:04, 11 March 2010 (UTC)[reply]

External links modified[edit]

Hello fellow Wikipedians,

I have just modified 2 external links on List of derivatives and integrals in alternative calculi. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 18 January 2022).

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 20:15, 29 December 2017 (UTC)[reply]