It is well known that the automorphism group Aut(H) of the algebra of real quaternions H consists entirely of inner automorphisms i(q) : p -> q . p . q(-1) for invertible q is an element of H and is isomorphic to the group of rotations SO(3). Hence, H has only inner derivations D = ad(x), x is an element of H. See  for derivations of various types of quaternions over the reals. Unlike real quaternions, the algebra H-d of dual quaternions has no nontrivial inner derivation. Inspired from almost inner derivations for Lie algebras, which were first introduced in  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 H-d become a derivation and show that the dual quaternion algebra H-d consists of only central derivations. We also show how a coset invariant central derivation of H-d is closely related with its spectrum.