It is our purpose here to show the deep relationship between differential rates and their underlying information sets. To accomplish our task, we will make for the following stages: In the first place, we deal with scaled changes along a period and conditional rates of change within a discrete environment. Next, rings and algebras of sets are addressed, so as to provide information sets with a suitable structure and give grounds to differential rates. Afterwards, differential rates are presented rigourosly, and two important lemmas follow through: the first one makes possible the use of differential rates with restrictive assumptions on their information sets, as customary applications seem to require. The second lemma attempts a broader outcome in a general setting so as to cope with differential rates defined on more realistic information sets. Both lemmas contributerigorously to shape definitions of narrow and broad differential rates on residual information sets.