Derivatives using cubic spline interpolation in C#

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C#

I am writing in a program in C#. I have 60 values (torsional eigenmodes of a wind turbine tower) and my supervisor asked me to find derivatives of these 60 values at respective 60 points using Cubic Spline Interpolation. There are total 60 nodes/points in a tower. For each section between two nodes, a torsional eigenmode value is assigned to it. I need to find the derivatives of these torsional eigenmode values by using spline interpolation. Curves are drawn between every two nodes using torsional eigenmode values and the tangent to each curve is the derivative for that particular torsional eigenmode value. A polynomial is defined for each curve.I need to write methods in the program to calculate these derivatives. I looked on the internet for spline interpolation and there are many different codes and explanations, so I dont know which one to select or study.Can anyone please guide me by pointing me out to an authentic internet link or can somebody give me the particular code. Thank you!

What I have tried:

I looked on the internet for spline interpolation and there are many different codes and explanations, so I dont know which one to select or study.