  We apply the direct variational method to derive the equation of state for
finite nuclei within the stability valley. The extended Thomas-Fermi
approximation for the energy functional with Skyrme forces is used. Using the
leptodermous expansion for the profile nucleon densities, we have studied the
neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using
equation of state for the pressure, we derive the region of spinodal
instability of finite nuclei and its dependence on the mass number, the
asymmetry parameter and the Skyrme force parameters. We suggest the procedure
of derivation of the isospin symmetry energy from analysis of the isospin shift
of chemical potential $\Delta\lambda = \lambda_n - \lambda_p$ beyond the
beta-stability line.
