I found a reference to Malcev (1949): for each ordinal number $\aleph$ exist a hypoabelian group with derived length $\operatorname{der}(G)=\aleph$.
In particular: for each $n\in\mathbb{N}$, exists a soluble group G with derived length $\operatorname{der}(G)=n$.
I ask how one can construct an easy exemple (if possible the easiest).
Ps. I know that dihedral group $G=D_{2^{n+1}}$ is nilpotent with class of nilpotence $\operatorname{cl}(G)=n$ and that in general $\operatorname{der}(G)\le \operatorname{cl}(G)$. Perhaps in this case they are equal?