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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?

buujek
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    This is hard to follow. What are the $x_i$ and what have they got to do with $f(x)$? In any case, the derivative of $f(x)=x^2$ is $f'(x)=2x$, there is no additive constant involved with derivatives (there is with integrals, but that's a different story). – lulu Mar 31 '24 at 23:55

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