Construct · 1 fields · 1 citations

derivative: a standalone construct

One name. One construct. A landmark on the map.

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derivative1 CONSTRUCTDerivative (math)GRABINER · RATE OF CHANGE

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Mathematics

Instantaneous rate of change of a function

In calculus, the derivative of a function is its instantaneous rate of change at a point: the slope of the straight line tangent to the graph, found as the limit of the average rate of change over an interval as that interval shrinks toward zero, the limit of the difference quotient. Grabiner's 1983 The Changing Concept of Change: The Derivative from Fermat to Weierstrass traced how this idea grew from the tangent and maximum problems of Fermat, through the calculus of Newton and Leibniz, to the rigorous limit definition of the nineteenth century. Here the referent is a mathematical operation on a function, a number attached to each point, and it has nothing to do with a financial contract, a word built from another word, or a compound made from a parent substance.[1]

Unit
A number giving a function's rate of change at one point, in output units per input unit
Recovery means
Not applicable
Measured by
Computed as the limit of the difference quotient, or by the rules of differentiation applied to a function's formula

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Nearby constructs

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References

  1. Grabiner, J. V. (1983). The changing concept of change: The derivative from Fermat to Weierstrass. Mathematics Magazine, 56(4), 195–206. https://doi.org/10.1080/0025570x.1983.11977043

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