Abzuleiten

Abzuleiten is the infinitive form of the German verb ableiten with the prefix ab- and is used primarily in formal or technical language. The core idea is to derive, deduce, or obtain a conclusion or property from other facts, data, rules, or a given equation. In this sense, abzuleiten expresses that something follows logically or computationally from something else.

In mathematics and the sciences, ableiten normally denotes differentiation (the calculus operation). The form abzuleiten can appear when describing that a conclusion or consequence can be derived from a formula, data set, or argument, but the common verb for the calculus operation remains ableiten, with the noun Ableitung. A typical construction is: Aus der Gleichung lässt sich ableiten, dass die Lösung negativ ist. Another formal usage is: Es ist aus den Beobachtungen abzuleiten, dass ein Trend besteht. In everyday language abzuleiten is relatively rare compared with ableiten or herleiten, and it tends to carry a more deliberately formal or written tone.

Etymologically, abzuleiten combines leiten (to lead) with the prefix ab- (away, deriving from) and the infinitive marker zu in certain constructions. The overarching sense is the act of deriving a result, conclusion, or derivative from a prior basis.

See also: Ableitung, Herleitung, Deduktion, Ableiten (in mathematics).