This paper concerns with generalized differentiation of set-valued and nons
mooth mappings between Banach spaces. We study the so-called viscosity code
rivatives of multifunctions and their limiting behavior under certain geome
tric assumptions on spaces in question related to the existence of smooth b
ump functions of any kind. The main results include various calculus rules
for viscosity coderivatives and their topological limits. They are importan
t in applications to variational analysis and optimization.