We have studied the compression properties of a finite nuclear system in the relativistic mean-field theory. Calculations have been carried out in the framework of the relativistic Thomas-Fermi approach. We have considered the derivative scalar coupling for the isoscalar sigma meson. It is shown that in the derivative coupling, the relativistic mean field leads to surface compression properties very close to those of the standard Skyrme interaction SkM*. This shows that at about the saturation point the derivative coupling exhibits a behavior close to SkM*. The high-density trend of the derivative coupling, however, diverges from that of SkM*.