  The purpose of the present paper is to investigate cohomologies and
deformations of weighted Rota-Baxter Lie algebras as well as weighted
Rota-Baxter associative algebras with derivations. First we introduce a notion
of weighted Rota-Baxter LieDer and weighted Rota-Baxter AssDer pairs. Then we
construct cohomologies of weighted Rota-Baxter LieDer pairs, weighted
Rota-Baxter AssDer pairs and we discuss the relation between their cohmologies.
Finally, as an application, we study deformations of both of them.
