It is well known that the automorphism group Aut(H) of the algebra of real quaternions H consists entirely of inner automorphisms iq : p → q ·p·q −1 for invertible q ∈ H and is isomorphic to the group of rotations SO(3). Hence, H has only inner derivations D = ad(x), x ∈ H . See [4] for derivations of various types of quaternions over the reals. Unlike real quaternions, the algebra Hd of dual quaternions has no nontrivial inner derivation. Inspired from almost inner derivations for Lie algebras, which were first introduced in [3] in their study of spectral geometry, we introduce coset invariant derivations for dual quaternion algebra being a derivation that simply keeps every dual quaternion in its coset space. We begin with finding conditions for a linear map on Hd become a derivation and show that the dual quaternion algebra Hd consists of only central derivations. We also show how a coset invariant central derivation of Hd is closely related with its spectrum.