  This paper studies biderivations on finite-dimensional complex semisimple Lie
algebras to their finite-dimensional modules. More precisely, we prove that all
such symmetric biderivations are trivial. As applications, we determine all
biderivations on Takiff algebras and symplectic oscillator algebras, as well as
all supersymmetric biderivations over some Lie superalgebras including all
finite-dimensional classical simple Lie superalgebras.
