  We discuss some analytical and numerical aspects related to the replacement
of integral dispersion relations by derivative relations and also the practical
applicability of the derivative approach in the investigation of high-energy
elastic hadron-hadron scattering. Making use of a Monopole Pomeron model and
singly subtracted integral and derivative dispersion relations, we present the
results of fits to the experimental data on the total cross sections and the
ratio of the real to the imaginary part of the forward elastic scattering
amplitude (proton-proton and antiproton-proton interactions). The emphasis is
on the region of low energies and, in particular, we show that once the
subtraction constant is used as a free fit parameter the derivative approach is
equivalent to the integral approach even below the energy cutoff of the fitted
data.
