TITLE: Derive or differentiate?
QUESTION [27 upvotes]: 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

REPLY [2 votes]: In mathematical/Calculus sense only: to differentiate is the verb "to find or calculate the derivative"
The noun is "the derivative"
Non-calculus students assume that it's ok to say or ask "how do I derive this function?" NO! Calculus students ask, "How do I differentiate this function?" Or "How may I find the derivative of this function?"
Conclusion: right now, in the 21st century Calculus instructors use the verb = differentiate and the noun = derivative