Talk:Differentiable function

Merger proposal

Should local linearity be merged into differentiable function? In the context of analysis, "locally linear" is a synonym for (and possibly the best way of thinking about being) "differentiable". I don't think much of the content at local linearity is useful: it would mostly be adding a sentence somewhere in this article and turning local linearity into a redirect. — Preceding unsigned comment added by Xnn (talk • contribs) 16:26, 28 July 2012 (UTC)

 DoneCactus0192837465 (talk) 13:40, 3 September 2018 (UTC)

No definition?

I think the most important part of the article is missing: There is no where in the article a formal definition of differentiability of a function over a point. Or over his domain.Santropedro1 (talk) 23:07, 4 May 2013 (UTC)

 DoneCactus0192837465 (talk) 13:39, 3 September 2018 (UTC)

Multivariate

The intro says "For a function of several real variables, there is no notion of derivative." How is the Jacobian matrix not a "notion of derivative"? I don't think the line does anything else except confuse. Tomtheebomb (talk) 05:37, 25 January 2014 (UTC)

 Done Cesiumfrog (talk) 06:09, 25 January 2014 (UTC)

Use of the term "bend"

What is meant by the term "bend"? I think it is likely to give the wrong impression. The graphs of many differentiable functions "bend".

Thanks

Aliotra (talk) 00:46, 4 April 2019 (UTC)

Where is H defined?

The variable h is used in multiple places, for example in the discussion on complex numbers. I haven't been able to find it's identification anywhere on the page. mbuc91 (talk) 14:56, 26 May 2019 (UTC)

@Mbuc91: It's part of a limit, and so not defined outside the scope of each limit it's used in. –Deacon Vorbis (carbon • videos) 15:59, 26 May 2019 (UTC)

"Differentiability" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Differentiability. Please participate in the redirect discussion if you wish to do so. 1234qwer1234qwer4 (talk) 10:09, 29 April 2020 (UTC)

"Continuously differentiable" listed at Redirects for discussion

A discussion is taking place to address the redirect Continuously differentiable. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 October 17#Continuously differentiable until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 𝟙𝟤𝟯𝟺𝐪𝑤𝒆𝓇𝟷𝟮𝟥𝟜𝓺𝔴𝕖𝖗𝟰 (𝗍𝗮𝘭𝙠) 21:21, 17 October 2020 (UTC)

"Nowhere differentiable" listed at Redirects for discussion

The redirect Nowhere differentiable has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 May 16 § Nowhere differentiable until a consensus is reached. Randi Moth ^Talk_Contribs 22:22, 16 May 2023 (UTC)

Isn't the formal differentiable definition wrong ?

Shouldn't it include the requirement that left derivative = right derivative at the point ?

By the current definition, the absolute function is differentiable at 0 (the limit, which is actually for the right derivative, exists - it's 1...), while this page itself claims that it is not... ScienceIsGolden (talk) 14:55, 22 March 2024 (UTC)

The derivative at 0 of the absolute function is defined (here and everywhere) as $\lim _{h\to 0}{\frac {|h|}{h}}.$ As this fraction is 1 for $h>0$ and 0 for $h<0,$ the limit does not exists. In other words, the derivative exists if and only if the left derivative and the right deirivative exist and are equal. That is, the requirement that "left derivative = right derivative" is included in the definition of the derivative. D.Lazard (talk) 15:18, 22 March 2024 (UTC)

Thanks, I figured it and just came back to delete my question... but you were faster... tx again ! ScienceIsGolden (talk) 15:54, 22 March 2024 (UTC)