Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

When the action is: Taking the derivative

what verb should be used?

  • to differentiate

  • to derive

I feel that deriving is not the correct word here. In my mind it's more a synonym of deducing. Am I right or has the word derive got the same meaning as differentiate? Or perhaps differentiate is not a proper English word...? If so, can anyone name a book or article where the writer(s) (preferably native English speaker(s)) use the word derive to mean differentiate? Or should we always stick to saying: "Take the derivative of..."?

Edit: So from what I can tell, the phrase: "Derive a method for differentiating this function and write down the resulting derivative.", can only have one meaning. XD

share|improve this question
2  
The correct verb is to differentiate. The corresponding noun is differentiation. The mathematical meaning of 'to differentiate' ca be found through google (it's no. 3) –  Danu Jul 10 at 11:48
    
I'm not 100% sure this is canonical, but you either take a derivative or differentiate. 'Derive' often means 'solve' or 'find a solution'. –  Alex Jul 10 at 11:49
    
Your summary sentence ("Derive how you should...") is a little awkward; more often that would be "Explain how you should..", or something like that. I recommend "Derive a method for differentiating this function and write down the resulting derivative." –  John Jul 10 at 17:55
2  
"Derive" and "differentiate" have different derivations, and it's important to differentiate between them ;-) –  David Jul 15 at 5:06
    
It probably comes about because “differential” can also be part of a car (making “differential equation” a misleading phrase for non-mathematicians). “derivative” is arguably a clearer word. The logic then goes that a derivative must have been derived from something. But surprisingly, it's not actually that common. I think, to a native speaker, “-tive” doesn't quite work to back-form a synonym for “differentiate”. –  James Wood Jul 15 at 23:05

2 Answers 2

up vote 12 down vote accepted

In English, I've almost always heard mathematicians say "We now differentiate $f$ to get ...". Occasionally I've heard "derive," but in English (my native language!), that's generally used to mean "work out", as in "Ralph couldn't derive a proof of the intermediate value theorem from the information he had at hand." It's also used in generating one thing from others, as in "We can now derive the half-angle formulas from the addition formula by a clever substitution."

share|improve this answer
    
I had a pretty strong feeling that this would be the case, but I've seen people doing it wrong so often, that I began doubting. –  gebruiker Jul 10 at 11:53
1  
I agree: I hear "derive" used for "differentiate" only by non-native speakers (of English, or of calculus). –  Greg Martin Jul 11 at 16:27

That is a question for a native speaker, I fear.

In German both are used

  • to differentiate = differenzieren (determing the derivative)
  • to derive = ableiten -> Ableitung (derivative)

In English literature, I think I only saw differentiate for the operation.

In German you can use "Herleitung" to stress more that it is about taking conclusions. In English it is maybe "derivation".

share|improve this answer
    
The same in French : both words are used with the same meaning ($differencier$ and $dériver$). –  Claude Leibovici Jul 10 at 11:55
    
I know what you mean. Also in my native language (Dutch) you can use the word afleiden. However the word has a double meaning; one of these meanings translates to differentiate, and the other to derive. I think that's the origen of confusion for most people... –  gebruiker Jul 10 at 11:56
    
Same in Swedish –  Vixen Jul 10 at 14:06

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.