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I'm not a native English speaker. A quick Google search revealed the symbol's name is apostrophe, just like in French. When used in a mathematical setting, I usually call it prime, so for instance f' I'll read $f$ prime. That's the way you call it in French, but I just realized I didn't actually know whether that was the way you call it.

Thank you!

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    As everyone is pointing names for this, in portuguese it reads "f linha" (literally, "f line") - and it is not an apostrophe nor a simple quote opening.2013-06-14

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It varies with the region.

"Prime" is how you pronounce it in American English. Here is a nice reference for American English pronounciations of math symbols; f' is on the top of the second page.

"Dash" is how you pronounce it in British English: Here (search for dash).

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    I fear the only “double dash” I've been taught in school is Mario Kart.2011-09-02
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$f'\rightarrow$ f prime

$f^{\prime\prime}\rightarrow$ f bis

$f^{\prime\prime\prime}\rightarrow$ f tris

$f^{\prime\ \backprime\prime}\rightarrow$ f tetrakis

However most people do not know these words and just say double prime, triple prime etc.

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    I agree with f bis, being common in Swedish education. The other's I've never heard, but I haven't seem them used in notation either, f^(n) being the norm.2013-10-18
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In high school and junior-high school in Japan, we read a' as "a dash". However, in universities, it is occasionally read as "a prime" due to American influence.

I am not native speaker of English; therefore, I explored dictionaries and found a description. The Oxford English Dictionary vol. XIII (1970) states that it "usually read as `a dash' " in the explanation of the word "prime". I feel something odd in this statement, but in the explanation of the word "dash" in OED vol. III (1969), I found that "a stroke or line (usually short and straight) made with a pen or like, or resembling one, so made ....". I am now realised the symbol ' should be recognized to be a short script.

I would like rather ask why American reads a" as double prime. Why the prime (= the most important) is not only one?

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    The main meaning of "dash" is "a short and rapid run". This perfectly matches the quick writing of a pen for adding ' adjacent to f, even though "prime" is an actual name of the symbol. Of course, I also use "f prime" when nobody understands "f dash". However, I don't feel "f dash" is a minority2017-03-01