# Find fit for complex function for smooth derivatives

I need to fit my data dropbox of the form {x,y} because I need the fit function for further derivative calculation. My derivative curve should be smooth.

I tried

 BSplineFunction[data, SplineDegree -> 5]


and also

Interpolation[data, InterpolationOrder -> 2]


but both derivates are not smooth.

Therefore I ended up by using least square fit (LSF) by using a polynomial with varying the degree of the polynomial (DOP) to find the best fit:

DOP = 21;
LSF = Fit[data, Evaluate[Table[x^i, {x, 0, DOP}]] , x];


The problem is that even choosing a high DOP, the experimental data are not fitted very well in the important section of the curve (between local minimum and -maximum)

(blue: experimental data; red: LSF)

and/or the derivative seems to start to oscillate at the beginning or end of the curve (in this example at the beginning, pointed to by black arrow):

Zooming the experimental curve in the first section does not reveal something that could cause that error:

Has that something to do with Runge's phenomenon or how can I solve that easily?

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Using Chebyshev nodes probably solves the problem... – Shukoff Nov 16 '13 at 17:52
You might want to look at this discussion? mathematica.stackexchange.com/a/10997/1089 – chris Nov 16 '13 at 17:54