  The interplay between derivations and algebraic structures has been a subject
of significant interest and exploration. Inspired by Yau's twist and the
Leibniz rule, we investigate the formal deformation of twisted Lie algebras by
invertible derivations, herein referred to as "InvDer Lie". We define
representations of InvDer Lie, elucidate cohomology structures of order 1 and
2, and identify infinitesimals as 2-cocycles. Furthermore, we explore central
extensions of InvDer Lie, revealing their intricate relationship with
cohomology theory.
