  We study the numerical differentiation formulae for functions given in grids
with arbitrary number of nodes. We investigate the case of the infinite number
of points in the formulae for the calculation of the first and the second
derivatives. The spectra of the corresponding weight coefficients sequences are
obtained. We examine the first derivative calculation of a function given in
odd-number points and analyze the spectra of the weight coefficients sequences
in the cases of both finite and infinite number of nodes. We derive the
one-sided approximation for the first derivative and examine its spectral
properties.
