  The description of deuteron-induced inclusive reactions has been an important
subject in direct nuclear reaction studies and nuclear data science. For
proton-induced inclusive processes, the semiclassical distorted wave model
(SCDW) is one of the most successful models based on quantum mechanics. We
improve SCDW for deuteron-induced inclusive processes and clarify the
importance of the proper treatment of the kinematics of the deuteron inside a
nucleus. The double differential cross section (DDX) of the inclusive
deuteron-emission process $(d,d^{\prime}x)$ is described by one-step SCDW. The
changes in the kinematics due to the distortion effect, the refraction effect,
is taken into account by the local semiclassical approximation (LSCA). The
calculated DDXs of $(d,d^{\prime}x)$ reasonably reproduce experimental data in
the small energy-transfer region and at forward and middle angles with some
exceptions. The angular distributions of $(d,d^{\prime}x)$ are improved by
including the refraction effect. The proper treatment of the changes in the
kinematics of the deuteron inside a nucleus is necessary in describing the
($d$,$d'x$) reaction. The effect of the changes on the DDX of $(d,d^{\prime}x)$
is significant compared to on the proton-induced inclusive process
$(p,p^{\prime}x)$ because of the stronger distortion effect on the deuteron.
