OK, after all those years of teaching calculus, it seems I've been saying it all wrong, or at least that is the opinion of several people on the AP calculus list who think that the verb "Derive" is not acceptable for "differentiate" which they suggest is better. I have even posted videos "I will Derive" parodies of the old "I will survive" song.
Ok, maybe they have a point...but I'm a little confused. If they want to get pedantic about not using "derive" then they certainly must avoid "derivative" (that which is derived, to obtain or receive from a source)..If you differentiate, then you get a differential; yes??? So if you want to find the derivative... well, you get my drift.
Derive is kind of a great word, it comes directly from the word river (which once meant the banks and not the river, hence the Riviera is the coast). In days of yore the draining of water out of the river and into the fields for irrigation was something like "derivering" and then worked its way into "deriving" (get it, to draw from a source). We use derive in that sense a lot in math for any type of deductive reasoning. To me it seems perfectly logical to talk about deriving the function for the slope from the original function, and calling the result of that derivation, the derivative.
Sorry guys, but I'm afraid that I've been doing it way to long to break the habit now, so I will continue to derive, but if I can remember I will try to tell my students that they may encounter a future professor who may dislike the usage, and they should be prepared for such an event... but honest, I don't much care which word they use, I just wish they would remember to apply the chain rule.