  The purpose of this paper is to introduce and investigate the notion of
derivation for quandle algebras. More precisely, we describe the symmetries on
structure constants providing a characterization for a linear map to be a
derivation. We obtain a complete characterization of derivations in the case of
quandle algebras of \emph{dihedral quandles} over fields of characteristic
zero, and provide the dimensionality of the Lie algebra of derivations. Many
explicit examples and computations are given over both zero and positive
characteristic.
  Furthermore, we investigate inner derivations, in the sense of Schafer for
non-associative structures. We obtain necessary conditions for the Lie
transformation algebra of quandle algebras of Alexander quandles, with explicit
computations in low dimensions.
