Numerical Derivative Formula: X's Not Same Distance

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SUMMARY

The numerical formula for a derivative when the x-values are not equidistant is approximated using the formula f'(x_{n}) ≈ (y_{n+1} - y_{n}) / (x_{n+1} - x_{n}). This method is a discrete approximation that varies in effectiveness based on the distribution of x-values. Caution is advised when applying numerical derivation to measurement data, as it can lead to significant noise interference if not handled properly.

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Hello,
What is the numerical formula for a derivative, considering the x's are not in the same distance?
 
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What do you mean by "numerical formula for a derivative" and which "x's" at which distances?

Do you have a discrete approximation for a function and try to approximate its derivative? There are multiple ways to do this, and the best one will depend on the application.Please stop making even more copies of this thread! I deleted the copies.
 
ddddd28 said:
Hello,
What is the numerical formula for a derivative, considering the x's are not in the same distance?
The best you can do is obviously [itex]f'(x_{n})\approx \frac{y_{n+1}-y_{n}}{x_{n+1}-x_{n}}[/itex].

There are better formulas, but then you have to know more about the distribution.

NB! Be very careful with numerical derivation of measurement data! Very often you subtract the significant part of the data and end up with the "noise" inherent in the data.
 

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