Question

What is "the derivative?"

Answer 1

Slope of any curve at a point is said to be derivative of the curve at that point.

Answer 2

The small change of a variable in respect to another variable is the derivative.
You could also say that it's the slope at any point.

Answer 3

remember how you found the slope when you had two points?

(y_1-y_0)/(x_1-x_0) imagine now that x_1-x_0 = 0

now instead of haveing the slope between two points we have the slope of one point

Answer 4

Much obliged gentlemen.