Talk:Semi-differentiability

Looking at the change logs, the direction in which h approaches 0 and whether h should be added or subtracted appears to be a common source of confusion, basically leading to a revert war. Please do not make this revert again without first discussing it here and refuting my point.

If in the two expressions, both the direction of approach changes AND the operation changes, then the two expressions are equal since adding a positive h and subtracting a negative h are the same thing. So EITHER the direction of approach must be different, OR the operation must be different, but not both.

My personal preference (and this is a matter of opinion) is for the direction of approach to be different, so that the resulting expression, (f(x+h)-f(x))/h, will remind us of the standard expression used for the standard, Calculus 1 definition of a derivative (though it would be equivalent to use x-h there too, my experience is that authors seldom, if ever, write it that way). The different one-sided limits thus suggest that this is a kind of "one-sided derivative."

I hope that this will help resolve the issue and that this part of the article will not be edited by people without first reading the discussion or the change logs, but that's wishful thinking.

--Phillist (talk) 22:40, 19 March 2008 (UTC)

Another thing, shouldn't it say, the first of the limits is equal to the other, not the opposite? Then the limit (as opposed to one-sided limits) exists, and hence the derivative, which is defined to be that limit. For example, in the absolute value function, the left derivative around 0, whose value is -1, is indeed the opposite of the right derivative around 0, whose value is +1. But absolute value is certainly NOT differentiable around 0. Identity, and not additive inverses, is the correct condition.

--Phill (talk) 19:51, 20 March 2008 (UTC)

You are right. The signs got flipped around that formula a few times without anybody synchronizing with the text below. Now it is all correct. Oleg Alexandrov (talk) 19:38, 13 April 2008 (UTC)

Left and right derivative

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

Merge Operator873^CONNECT 02:38, 4 October 2017 (UTC)

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The article Left and right derivative appears to be an inferior copy of this one, to the point where formulas appear to have been copied from here over there with insufficient explanation as to all the symbols involved. Also I don't see why two articles are needed on essentially the same topic. Some1Redirects4You (talk) 19:56, 26 April 2015 (UTC)

@Some1Redirects4You: I think merging these two is a sensible idea. However, there is one other use of left/right derivative mentioned at the bottom of the article which should be included in the merge; in physics, a derivative between a bra and a ket can act on the left or the right, and this is sometimes referred to as a left or right derivative. Only one article, Batalin–Vilkovisky formalism, links to this usage right now, though, so if you do take it out, it will be no great loss. Other than that, a merge definitely seems in order.Brirush (talk) 13:47, 29 April 2015 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

The merge proposal passed without opposition and has been accomplished. Operator873^CONNECT 02:38, 4 October 2017 (UTC)

Colleagues,

Am I missing something or the second statement in the section “Properties” (which is “While every semi-differentiable function of one variable is continuous…”) is dead wrong? A counterexample is provided by the picture at the beginning of the article.

Alexander 99.133.144.22 (talk) 19:46, 30 January 2022 (UTC)