  We discuss some formal and practical aspects related to the replacement of
Integral Dispersion Relations (IDR) by derivative forms, without high-energy
approximations. We first demonstrate that, for a class of functions with
physical interest as forward scattering amplitudes, this replacement can be
analytically performed, leading to novel Extended Derivative Dispersion
Relations (EDDR), which, in principle, are valid for any energy above the
physical threshold. We then verify the equivalence between the IDR and EDDR by
means of a popular parametrization for total cross sections from proton-proton
and antiproton-proton scattering and compare the results with those obtained
through other representations for the derivative relations. Critical aspects on
the limitations of the whole analysis, from both formal and practical points of
view, are also discussed in some detail.
