2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77162We define analogues of higher derivatives for $F_q$-linear functions over the field of formal Laurent series with coefficients in $F_q$. This results in a formula for Taylor coefficients of a $F_q$-linear holomorphic function, a definition of classes of $F_q$-linear smooth functions which are characterized in terms of coefficients of their Fourier-Carlitz expansions. A Volkenborn-type integration theory for $F_q$-linear functions is developed; in particular, an integral representation of the Carlitz logarithm is obtained.18 pages, LaTex-2e, to appear in Journal of Number TheoryNumber Theorytext