# Rate of Change - Derivative of experimental data

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Perri Johnson on 24 Jun 2022
Commented: Star Strider on 24 Jun 2022
Does anyone have any advice on determining the instantaneous rate of change for strain or force data for multiple cycles? If there is a wasy or function to help with taking the derivative of a curve in MatLab? I've tried using the diff() function but the results give me a value in the thouands when the peak instantaneous loading rate I received from LabView is only in the hundreds. I can attach my current code if you would like to see it, but unfortanutely I can't post the experimental data I have.
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Sam Chak on 24 Jun 2022
Perhaps considering to post only a fraction of the data, say 10 points, or 10% of the data (if not too large).

Star Strider on 24 Jun 2022
I usually do something like this —
This assumes the independent variable ‘x’ and the dependent variable ‘y’ are both vectors of the same length. See the documentation on gradient for details.
Star Strider on 24 Jun 2022
There are several options, among which is filloutliers that detects outliers and interpolates them. Like all signal processing tasks, you will need to experiment to get the desired result.

John D'Errico on 24 Jun 2022
Edited: John D'Errico on 24 Jun 2022
If your data is smooth enough, then the direct gradient calls that Star shows are ok. The problem is, if there is any noise in your data, then using the finite differences from gradient may be a bad idea, as they will amplify the noise. Then you will benefit form a Savitsky-Golay style of filter. The idea is to use a moving polynomial approximation at each point to estimate the slope.
I posted movingslope on the File Exchange, which does exactly that, allowing you to choose the length of the moving filter, as well as the local polynomial order.
However, I recall it assumes your data curve is equally spaced in x. If you lack equally spaced data in x, then if you have any noise, you can still do something, but it will be way less efficient.