the word $d_{\uu}(w) = s_0s_1s_2 \cdots$ is called the *derivated word of $\uu$ with respect to $w$*, introduced in [@Durand98]. A simple corollary of the characterization by return words and a result of [@Durand98] is that the derivated word $d_{\uu}(w)$ is also a Sturmian word (see ). This simple corollary follows also from other results. For instance, it follows from [@AraBru05], where the authors investigate the derivated word of a standard Sturmian word and give its precise description. It also follows from the investigation of a more general setting in [@BuLu], which may in fact be used to describe derivated words of any episturmian word — generalized Sturmian words [@GlJu].

By the main result of [@Durand98], if $\uu$ is a fixed point of a primitive morphism, the set of all derivated words of $\uu$ is finite (the result also follows from [@HoZa99]). In this case, again by [@Durand98], a derivated word itself is a fixed point of a primitive morphism.

In this article we study derivated words of fixed points of primitive Sturmian morphisms. By the results of [@MiSe93], any primitive Sturmian morphism may be decomposed using elementary Sturmian morphisms — generators of the Sturmian monoid. In , we describe 