  We use two non-perturbative methods to obtain the anisotropy derivatives of
the coupling constants (the anisotropy coefficients) of SU(3) lattice gauge
theory. These coefficients appear in the derivative formulae for the energy
density and the pressure. We calculate them for the standard Wilson and two
improved actions, the 2x2 and the Square Symanzik action. Both methods lead for
all investigated actions to compatible results which are clearly different from
their known asymptotic perturbative limits. With increasing beta the limits are
however approached in all cases. Our findings strongly support the equivalence
of the integral and derivative methods for the calculation of energy density
and pressure.
