  We study a class of tame $\mathcal{L}$-theories $T$ of topological fields and
their $\mathcal{L}_\delta$-extension $T_{\delta}^*$ by a generic derivation
$\delta$. The topological fields under consideration include henselian valued
fields of characteristic 0 and real closed fields. We show that the associated
expansion by a generic derivation has $\mathcal{L}$-open core (i.e., every
$\mathcal{L}_\delta$-definable open set is $\mathcal{L}$-definable) and derive
both a cell decomposition theorem and a transfer result of elimination of
imaginaries. Other tame properties of $T$ such as relative elimination of field
sort quantifiers, NIP and distality also transfer to $T_\delta^*$. As an
application, we derive consequences for the corresponding theories of dense
pairs. In particular, we show that the theory of pairs of real closed fields
(resp. of $p$-adically closed fields and real closed valued fields) admits a
distal expansion. This gives a partial answer to a question of P. Simon.
