Derivatives can refer to anything that is derived from something else, but here they refer specifically to functions that give the slope of the tangent line to a curve.
filler after a demonstrative pronoun but before the noun it modifies, solely for emphasis
You use here in order to indicate that the person or thing that you are talking about is near you or is being held by you. My friend here writes for radio
If you say that you are here to do something, that is your role or function. I'm not here to listen to your complaints
If something happens here and there, it happens in several different places. I do a bit of teaching here and there
You use here when you are pointing towards a place that is near you, in order to draw someone else's attention to it. if you will just sign here Come and sit here, Lauren
at this time; now; "we'll adjourn here for lunch and discuss the remaining issues this afternoon
in or at this place; where the speaker or writer is; "I work here"; "turn here"; "radio waves received here on Earth"
You use expressions such as `here we go' and `here we go again' in order to indicate that something is happening again in the way that you expected, especially something unpleasant. At first, he was told he was too young and I thought, `Oh, boy, here we go again.'