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I have same experimental data with same noise: enter image description here

I have to calculate the derivative and the integral of the function that fit the experimental data. I try with all the function in this page but the result was not good. How can I do that?

Update: I look for same method to interpolate the data in order to calculate the derivative and the integral of the "best fit function" (because data have same noise I can't compute directly the derivative of them). The problem refers to the fact that I can't find a function that fits "exactly" the data; I try with a combination of sine and cosine and other method but the result don't work well.

I read the Cross Validate guidelines and I think my question is more related to this site, but I can't migrate the question to it.

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    $\begingroup$ It seems your data doesn't nicely fit in a full function completely, but would fit some piecewise combination of several functions. However, I think it would be better to ask this on Cross Validated. $\endgroup$ – Discrete lizard♦ Apr 6 '18 at 15:29
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    $\begingroup$ Doesn't seem like a CS question to me; it's about applying numerical methods to noisy data. Computational Science may be a good place. Let me know if you want us to migrate. (cc @Discretelizard) $\endgroup$ – Raphael♦ Apr 6 '18 at 15:49
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    $\begingroup$ That said, what's the meaning of the derivative of this function? I suspect you really want to investigate a suitably smoothed function to discover trends. (Since your data are discrete, you can plot the point-by-point differences. I expect them to be useless, i.e. mostly noise.) $\endgroup$ – Raphael♦ Apr 6 '18 at 15:50
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    $\begingroup$ What do you mean by "the derivative and the integral of the function that fit the experimental data"? What do you mean by "the function that fit the experimental data"? That's not well-defined. There might be many functions that fit the data with some amount of error. What specifically does "not good" mean? What are you really trying to accomplish? Please edit your question to provide more explanation, context, and details. It might help to tell us what approaches you considered, why you rejected them, and use that to figure out what your requirements are. $\endgroup$ – D.W.♦ Apr 6 '18 at 19:37

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