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I am looking for an algorithm to calculate the derivative of functions like i=f(v). Do you know if this is somewhere publicly awailable?

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There are Mathematics ways to calculate the derivative of GOOD functions. (like Sin , Cos , tan, log etc.)

In this way you can calculate the derivative Exactly. ( Here I mean Exactly as Math. Exactly )

For Ex. Sin(a)` = Cos (a) , Cos(a)` = -Sin (a) etc. (There only About 20 Formulas)

But If you have not GOOD (Normal) Function so you can't calculate the derivative Exactly.

And You have only Approximately Methods. (From Array of Variables and not from Function )

Physics Ex:

We know velocity of Car In Each Second. And we want to Calculate the Acceleration in Each Sec.

Time: (Sec) 0 1 ....i ... n

Velocity:(M/s) V(0) V(1) ...V(I).. V(n) (In array V: Element V(i) it`s Velocity at Sec i )

SR: Sampling Rate ( In Our Example is Each Sec => SR = 1 )

The A(i) - acceleration at momet i (at Sec i ) equal to V` (derivative of V)

A(i) = V` = ( V(i)-V(i-1) ) / SR

I Hope It`s will help you.