  We construct (generalized) logarithmic derivatives for general n-dimensional
local fields K of mixed characteristics (0,p) in which p is not necessarily a
prime element with residue field k such that [k:k^p]=p^{n-1}. For the
construction of the logarithmic derivative map, we define n-dimensional rings
of overconvergent series and show that - as in the 1-dimensional case - they
can be interpreted as functions converging on some annulus of the open unit
p-adic disc. Using the generalized logarithmic derivative, we give a new
construction of Kato's n-dimensional dual exponential map.
