ableiten

Ableiten is a German verb meaning to derive or deduce. It is used in everyday language to indicate drawing a conclusion from evidence, or obtaining something from a source. In scientific and technical contexts, the term also covers the act of obtaining a related result or form from an original, such as a derivative or a related substance. The noun forms associated with the verb include Ableitung (derivative) and Ableitungen (derivatives).

In mathematics, Ableitung refers to the derivative of a function. The derivative measures how a function changes as its input changes and is a central concept of calculus. Differentiation yields a new function that describes the rate of change, such as the slope of a curve at a given point. Notation includes symbols like f′(x) or df/dx. Derivatives are used to solve problems in physics, engineering, economics, and beyond, including speed, optimization, and sensitivity analyses.

Beyond mathematics, Ableiten appears in logic and reasoning to denote deriving conclusions from premises, i.e., inferring what follows from given assumptions. In linguistics, derivation (Ableitung) describes the formation of new words from existing bases through affixation or other morphological processes. In chemistry, a derivative (Ableitung) is a compound that is structurally related to a parent substance by a defined modification.

The term derives from the German verb leiten (to lead) with the prefix ab-, signaling extraction or departure, and it is widely used across disciplines to indicate obtaining a result that follows from an initial source.