  This paper generalizes the concepts of 2-local derivations and biderivations
(without the skewsymmetric condition) of a finite-dimensional Lie algebra from
the adjoint module to any finite-dimensional module, and determines all 2-local
derivations and biderivations of the 3-dimensional complex simple Lie algebra
$\frak{sl}(2)$ on its any finite-dimensional simple module.
