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In mathematics, to derive a statement is to use logic, starting from known facts, or at the very beginning, from axioms, to decide whether the statement is true or false.

Formally, if you have a set of axioms A, then a set of statements B are all said to be derived if they follow logically from statements in A. And further, a set of statements C are said to be derived if they follow from statements in A and B.

DERIVE (TM) is the name of a commercial computer algebra system made by Texas Instruments.