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a mathematical expression with differentials in it

How do you read the differential mark?

4 Answers 4

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Formally, The derivative of...

In full:

Y equals the sine of f-of-x, implies that the derivative of y equals cos f-of-x times the derivative of f of x.

Informally, and depending on dialect, you can say either 'prime' (as per Humbulani's answer) or 'dash' - f prime of x, y-dash etc. The former is predominant in (but is not restricted to) the US, while the latter is relatively common in the wider Anglosphere.

Refer to: How do you pronounce the symbol ' in f'? and What is the practical difference between a differential and a derivative? for further information.

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    I also have a math degree and have never heard 'dash' as a term for differentiation.
    – Hellion
    Dec 14, 2014 at 16:04
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    @Humbulani: I am a professional mathematician and I have personally heard other professional mathematicians say "dash" in this context. I am trying to remember who it was and what dialect of English they spoke. Probably British English - it definitely wasn't American English. Dec 14, 2014 at 18:02
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    A simple test to check whether dash is in use is to google for "f double dash". Among other links (which seem to come from all over the world: UK, NZ, FI, IN, BE, GR, AU, etc.; I can't tell much about US but I can see a lot of .com and .net links) is one from Math.SE stack: math.stackexchange.com/questions/47339/…. Dec 14, 2014 at 18:26
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    @Humbulani: I personally call it "prime"; I am a native American English speaker and I would agree that "prime" is the correct term in American (mathematical) English. But there are lots of other dialects - as I said, I have definitely heard "dash" although I am not sure which dialect to associate it with. In any case, I would certainly not advise you to draw conclusions about what "nobody among mathematicians says" without broader experience! Dec 14, 2014 at 20:52
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    @J.R. It's not rare, it's dialectal. Or to put it another way, it's rare in some places but common in others.
    – user230
    Dec 15, 2014 at 8:12
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f′(x)

is read

  • f prime of x, or
  • the derivative of f of x, or
  • the derivative of f with respect to x.

f″(x)

is read

  • f double prime of x, or
  • the second derivative of f of x, or
  • the second derivative of f with respect to x.

is read

  • x dot, or
  • the derivative of x with respect to time, or
  • the time derivative of x.

If x is a distance, ẋ can also be read as the x component of the velocity.

If x is a distance, and is also the only direction of motion, ẋ can also be read as speed or velocity.

is read

  • x double dot, or
  • the second derivative of x with respect to time.

If x is a distance, ẍ can also be read as the x component of the acceleration. If x is a distance, and is also the only direction of motion, ẍ can also be read as acceleration.

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This mark means the first derivative of f. You can also call it a derivative of f. It is definitely wrong to call it the differential mark. American mathematicians read it as 'prime'. For example, f' (x) - f prime of x.

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  • In British English that is how I have heard it pronounced as well. Dec 15, 2014 at 13:22
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In high school and junior-high school in Japan, the symbol x' is usually pronounced as "x dash". However, in universities it is also read as "x prime". I think teachers in university are strongly influenced by Americans. I read it in both ways in a university.

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