afledningen

Afledningen is a Danish term that has multiple senses depending on the field. In linguistics, afledning refers to the process of forming new words from a base by derivational affixes, rather than by compounding. It is a central aspect of morphology and helps expand the lexicon by shifting meaning or grammatical class. It is distinct from sammensætning, the process of forming new words by linking two existing words. Danish derivation commonly uses suffixes such as -ning, -hed, -lig, and -er to create nouns and adjectives; for example, -ning can form a noun denoting an action or state (læring from lære).

With regard to mathematics, afledningen denotes the derivative of a function, i.e., its instantaneous rate of change. In calculus, the afledning f'(x) is defined as the limit of the difference quotient as h tends to zero. The derivative is a foundational concept used to determine slopes, velocities, and rates in models. Notation includes d/dx f(x) and f'(x); standard rules include linearity, the product rule, and the chain rule. For instance, the derivative of x^2 is 2x.

These senses reflect a common underlying idea: producing a new entity that follows from an existing one, though they apply to language and mathematical analysis respectively.