Define derivative from 3 perspectives?

[physicszman]

Define derivative from 3 perspectives?

I might be off but I only came up with slope and rate of change?
Is this correct? Whats the 3rd one?

Thanks for any help in advance !!!

[matt grime]

linearization

[HallsofIvy]

Slope of the tangent line.

(Which is just a different way of saying what matt grime said.)

[matt grime]

How about "the reverse of integration (on continuous functions)"

Or an element of Der(C^(oo)(R)) if you want to be fancy.

OK so that's what differentiation is, not exactly the same as the derivative.