I have a question about terminology. See this is what happens: someone says "this function is derivable", and then another, more experienced Anglo-Saxon mathematician goes on to correct this someone, saying that the term is "differentiable". Or at least in my experience. However, in Spanish (and other romance languages I believe), the situation would be: "this function is derivable", then the more experienced, romantic-language mathematician goes "yes, but that doesn't make it differentiable".
This is because, in Spanish, the term derivable means just that, the directional derivatives all exist, they just may not be a linear map of the direction. For example, in 1D "derivable" and "differentiable" would be the same thing (in fact this is a common stress point in lessons, how "it's not the same in higher dimensions!"). Furthermore, in 1-var. calculus I was urged to use the term "derivable", as opposed to "differentiable", so as to not gain a false understanding of the meaning of differentiability.
Call it a trifle, but I've really been wondering about this for my whole math education (and other things about real math, not to worry). So I ask if there is an analogue to "derivable" in English or if you have to work up a long phrase every time.
Best Answer
Why it's that way
From this wonderful site Earliest Known Uses of Some of the Words of Mathematics. See especially the first paragraph I transferred below:
The reason that we use "derivative" the way we do is because of how it arrived in English, and that often leads to these puzzling inconsistencies in the way we use the words. It may well be that it enters other languages in alternative ways that allow you to use "derivable" in that language, but there is no reason to expect English to adopt the custom used by other languages just to make it consistent across languages.
(Probably) why English doesn't use "derivable"
I'm pretty much of the same feeling that Seth expressed: "derive" is a much more generic verb than "differentiate," and it doesn't seem sensible to look for excuses to use "derive" this way.