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algorithm to calculate the derivative

Posted on 1997-04-09
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Last Modified: 2011-09-20
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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Question by:ericj040697
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Msoft earned 50 total points
ID: 1249868
Hi,

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.
                                           



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Expert Comment

by:jos010697
ID: 1249869
You're basiscally correct; a better estimation of f'(x), given
f(x) (in any form), is

   (f(x+h)-f(x-h))/(2h)

kind regards,

Jos
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