ABSTRACT
Derivatives are studied in the standard course of calculus. Is it possible, and how does one calculate a derivative of such a function? Everything depends on the type of data. If the data represents exact values of a function, it is better to use an interpolation. It is possible to calculate the derivatives on the basis of the interpolation. The polynomial interpolation and its derivatives are shown by means of a dashed line, whereas the function sin by a solid one. One can see that the function and its derivatives are accurately calculated. It is related to too acute oscillations of the interpolation function what causes significant deviations of the derivative. In such a case it is better to smooth data and afterwards to calculate the derivative. Other interpolations can be constructed by use of the different polynomials by fitting polynomial curves between successive data points. Mathematica selects the optimal interpolation in each case.
