Tapering optimization schemes for TeraWatt (TW) level X-ray Free Electron Lasers (FELs) are critically sensitive to the length of individual undulator and break sections. Break sections can be considerably shortened if the focusing quadrupole field is superimposed on the undulator field, increasing the filling factor and the overall extraction efficiency of the tapered FEL. Furthermore, distributed focusing reduces the FODO length and allows one to use smaller beta functions, reducing particle de-trapping due to betatron motion from the radial tails of the electron beam. We present numerical calculations of the tapering optimization for such an undulator using the three dimensional time dependent code GENESIS. Time dependent simulations show that 8 keV photons can be produced with over 3 TW peak power in a 100m long undulator. We also analyze in detail the time dependent effects leading to power saturation in the taper region. The impact of the synchrotron sideband
growth on particle detrapping and taper saturation is discussed. We show that the optimal taper profile obtained from time independent simulation does not yield the maximum extraction efficiency when multi-frequency effects are included. A discussion of how to incorporate these effects in a revised model is presented.