Can the word "derive" be used to mean "take the derivative of"?

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.

Here is an illuminating xkcd forum thread on the topic. People (myself included) seem to agree that the word 'derive' is incorrect.