Origin of the term "derived subgroup" The commutator subgroup G', generated by all commutators of a group G, is also called the derived subgroup. Why is this; are there any concrete analogies with analytical derivatives (apart from the notation) which justify this name, or is this merely an established expression?

In groupprops one can find the following historical remark: 
The notion of derived subgroup or commutator subgroup naturally arose in the context of finding a natural choice for a good composition series for a solvable group.
The result is the derived series, with $G$, $[G,G]$, $[[G,G],[G,G]]$ etc.
