derives

Derives is the third-person singular present tense of the verb derive. The core sense is to obtain something from a source, to deduce or infer, or to originate from something else. In everyday use, one might say a conclusion is derived from evidence, or a product derives from earlier designs. The word derives from Latin derivare, meaning to draw off or detach.

In linguistics and word formation, derivation is the process of creating new words from a base form by adding affixes or making other changes. A word “derives” from another when it can be traced back to that base form, such as unhappy deriving from happy with the prefix un-. This sense emphasizes origin and formation rather than mere copying.

In mathematics, the noun derivative is standard, describing the instantaneous rate of change of a function. The verb derive is used in describing the act of obtaining a derivative or formulating a result from principles, for example, to derive a formula by differentiation. The derivative is denoted by f′(x) or dy/dx and relates to the slope of the tangent line to the function’s graph; it is central to rules of differentiation and to connections between differentiation and integration through the fundamental theorem of calculus.

In chemistry, a derivative refers to a compound that is structurally related to another by a chemical modification. A compound may be described as a derivative of a parent compound, indicating its origin or relationship.

In logic and reasoning, one derives conclusions from premises through a process of deduction, argument, or inference. See also derivative, derivation, derivable.