Derive vs. Differentiate

[Cauchy]

I couldn't find something like this in the forum, so here goes.

What do people usually say for the act of finding the derivative of a function? I either say "differentiate" or "take the derivative of", but a lot of students I've worked with use "derive", and I have to wonder how widespread that usage is.

On a related note, why is the technical term "differentiate" if what you get is a "derivative"? Are these words related in any way?

[raptor.fortress]

I've not thought about it this deeply.

I usually say "find the derivative of" or "differentiate the following" rather than "derive this function"

I usually say something was derived from something else. This equation was derived from that one. Or you'll hear a lecturer say "this is derived from Bernoulli's equation".

or something like that.

[Cosmologicon]

The correct term is "differentiate". The incorrect term is "derive". It's a very common error. (You say you want to know how common, but I don't think you're going to get more quantitative than that.)

They're not related etymologically. Derive comes from the Latin word for "draw off", which itself comes from the word for "from the stream". Differ comes from the Latin words for "move apart".

[defaultusername]

I say differentiate. To differentiate is to derive, but to derive isn't necessarily to differentiate. To derive something can mean a lot of things, as raptor said.

Edited for grammar and spelling

[Ended]

I suspect the confusion stems from the fact that we call df/dx the "derivative" of f.

A derivative is something which derives from something else; equivalently, which is derived [from something else].

So it is inconsistent to say that we derive f. It would make more sense to say "we derive df/dx [from f]".

[headprogrammingczar]

I suspect the confusion stems from the fact that we call df/dx the "derivative" of f.

Theoretically, it would be just as easy to call df/dx the differential of f, eliminating the issue entirely.

[Ended]

I suspect the confusion stems from the fact that we call df/dx the "derivative" of f.

Theoretically, it would be just as easy to call df/dx the differential of f, eliminating the issue entirely.

Indeed, although "differential" currently has a (slightly different) meaning. But I think that "differential quotient" is sometimes used.

[skeptical scientist]

They're not related etymologically. Derive comes from the Latin word for "draw off", which itself comes from the word for "from the stream". Differ comes from the Latin words for "move apart".

It is important to use the word differentiate rather than derive to differentiate finding derivatives from deriving true statements. Their derivations are irrelevant; the important thing is being clear.

[doogly]

I suspect the confusion stems from the fact that we call df/dx the "derivative" of f.

Theoretically, it would be just as easy to call df/dx the differential of f, eliminating the issue entirely.

No good, the differential of f is df.

[Cosmologicon]

They're not related etymologically. Derive comes from the Latin word for "draw off", which itself comes from the word for "from the stream". Differ comes from the Latin words for "move apart".

It is important to use the word differentiate rather than derive to differentiate finding derivatives from deriving true statements. Their derivations are irrelevant; the important thing is being clear.

That reminds me when I played this quiz computer game (YDKJ) and the lightning round category was "what's my derivative?". I didn't know whether it was going to be about calculus or linguistics, but either way I was going to do pretty well. But then it turned out to be about narcotics.

[nahkh]

As a non-english speaker I run into this quite often, because the finnish term for taking a derivative of something is "derivoida" (obviously borrowed from english). If we want to derive something we say "johtaa" (a word native to finnish). It's fairly confusing. We use the term "differentioida" (to differentiate) only when discussing multi-variable functions.

[Monika]

Is "differentiate" used for other things besides finding the derivate? Like, to separate something into various groups (for example in a class have a sub-group of students with less skills do easier tasks)?

In German, we say "ableiten" (verb) and "Ableitung" (noun) for f '(x) and finding it. It's really a general word meaning to derive something. But now it's mostly only used for this ... for deriving something in general (a formula, a solution) we use "Herleitung". One can also say "differenzieren" instead of "ableiten", but there is no equivalent noun.

[erik542]

I suppose f' is called a derivative because it is derived from f through differentiation. In a more linguistic sense, A being a derivative of B has a tendency to mean that A is smaller than, but similar to B. So it sort of makes some kind of sense.

[Xanthir]

Is "differentiate" used for other things besides finding the derivate? Like, to separate something into various groups (for example in a class have a sub-group of students with less skills do easier tasks)?

Yes it is, and it has precisely the definition you give. As in: "The task at hand here is training a neural net to reliably differentiate between pictures containing kittens and pictures containing puppies."

[Cosmologicon]

"Differentiation" and "integration" are both buzzwords referring to types of instruction in the "ed biz". And they're not quite opposites, so you can have differentiated integrated instruction.

[Monika]

"The task at hand here is training a neural net to reliably differentiate between pictures containing kittens and pictures containing puppies."

Which so far AIs don't seem to be able to do

[Xanthir]

"The task at hand here is training a neural net to reliably differentiate between pictures containing kittens and pictures containing puppies."

Which so far AIs don't seem to be able to do

Incorrect! Machine Learning Attacks Against the Asirra CAPTCHA

[kgrizzly]

Would it be off topic to mention a pet peeve of mine that this thread reminds me of?

People who say "high rate of speed", a phrase brought to you by the Department of Redundancy Department. People say this when they really mean "high speed". For speed is a rate (miles per hour, distance/time). It might make more sense if they were talking about acceleration (rate of change of speed), but it's clear that's not what people usually mean when they say it. When I hear people use this phrase, I'm tempted to say, "Don't you really mean `high rate of speed of velocity'?"

[My Settings]

I thought the two words had different origins historically (not completely sure, been awhile since I took a course in the history of maths):

Derive: From French derivée. Fermat(or someone else) replaced all instances of a variable "x" in a statement with "x+e". Then equated the two statements and with a bit of hand-waving set e=0 and got a maximum. Add to this method and you get the derivative of a function.

Differentiate: To look at differences. Leading to difference-quotients and then differentials.

Am I completely off track here?