Do I understand derivatives correctly? As I understand it, derivatives are something like that in the example: f(x) = x^2:
x1=1, so 1
x2=4, so 3
x3=9, so 5
And the derivative is 2x+C, where C = -1. Is this some kind of overly successful example, or did I just misunderstand everything? This does not work with the example x^3/3, where the derivative x^2 does not match in any way. Why?