  The purpose of this paper is to extend the cohomology and conformal
derivation theories of the classical Lie conformal algebras to Lie conformal
superalgebras. Firstly, we construct the semidirect product of a Lie conformal
superalgebra and its conformal module, and study derivations of this semidirect
product. Secondly, we develop cohomology theory of Lie conformal superalgebras
and discuss some applications to the study of deformations of Lie conformal
superalgebras. Finally, we introduce generalized derivations of Lie conformal
superalgebras and study their properties.
