Assume we have a noisy data set with ##N## data points, ##x_i##, where ##i = 1, \ldots, N##.
Then Savitsky-Golay smoothing is equivalent to locally fitting a polynomial about each ##x_i## (using some number of neighboring data points), then evaluating that polynomial to produce a new ##y_i##.
Savitsky-Golay differentiation is equivalent to locally fitting a polynomial about each ##x_i## (using some number of neighboring data points), then evaluating a derivative of that polynomial to produce a new ##z_i##. This is of course only interesting to do if the order of the derivative is less than the order of the polynomial used in the fitting.