  Given a cluster-tilted algebra B we study its first Hochschild cohomology
group HH1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra
such that B is the relation extension of C by E= Ext2(DC,C), then we prove that
HH1(B) is isomorphic, as a vector space, to the direct sum of HH1(C) with
HH1(B,E). This yields homological interpretations for results of the first and
the fourth author with M.J. Redondo.
