  The article is devoted to approximate, global and along curves
differentiability of functions over non-archimedean infinite fields with
non-trivial valuations. Fields with zero and non-zero characteristics are
considered. Spaces of differentiable functions are defined with the help of
partial difference quotients. Approximate differentiability is studied relative
to real-valued measures. Theorems about relations between these three types of
differentiability are proved. Associated problem on extensions of such
functions is investigated.
