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Back when I was in high school, the usage of the word "derive" to mean "take the derivative of" was really widespread. It always bothered me because I felt that the proper verb should be "differentiate." I wondering if this use of "derive" is acceptable or not. Has anyone else heard the word "derive" used in this way?

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    I heard it for the very first time on MSE itself.2015-11-15

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I say "not acceptable".

I don't recall the grammatical/linguistic term, but it seems like "derive" in that sense needs a "from" somewhere: "This theorem can be derived from blah blah."

"Differentiate", on the other hand, can be used directly with its object: "let's differentiate $f$" and so on.

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    What about the derived group?2015-11-15
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Here is an illuminating xkcd forum thread on the topic. People (myself included) seem to agree that the word 'derive' is incorrect.