I'm using pythonnet (http://pythonnet.sf.net) to bind together a python framework and a .NET library (I know if IronPython but this is not the question).
Using pythonnet, I can create an Array ...
Finding "best-fit" derivatives for experimental data is often difficult since experimental variation can make the function look like it has "spikes" where the derivative goes nearly infinite (that's why integrating numerically is more reasonable -- the summation "smooths out" the variation). If you don't care about the degree of the polynomial you fit you can use Lagrange's interpolating polynomial. It will ...