Differential coefficient

Differential coefficient

In mathematics, the differential coefficient of a function f(x) is what is now called its derivative df(x)/dx, the (not necessarily constant) multiplicative factor or coefficient of the differential dx in the differential df(x).

A coefficient is usually a constant quantity, but the differential coefficient of f is a constant function only if f is a linear function. When f is not lineive#Differen, hence, the modern term, derivative.


Early editions of Silvanus P. Thompson's Calculus Made Easy use the older term. Martin Gardner lets the first use of "differential coefficient" stand, along with Thompson's criticism of the term as a needlessly obscure phrase that should not intimidate students, and substitutes "derivative" for the remainder of the book.


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  • Differential coefficient — differential dif fer*en tial, a. [Cf. F. diff[ e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster] For… …   The Collaborative International Dictionary of English

  • differential coefficient — n. DERIVATIVE (n. 5) …   English World dictionary

  • differential coefficient — noun the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx • Syn: ↑derived function, ↑derivative, ↑differential, ↑first derivative • Derivationally related forms: ↑differential …   Useful english dictionary

  • differential coefficient — Chiefly Brit. derivative (def. 6). [1810 20] * * * …   Universalium

  • differential coefficient — noun Mathematics another term for derivative …   English new terms dictionary

  • differential coefficient — /ˌdɪfərɛnʃəl koʊəˈfɪʃənt/ (say .difuhrenshuhl kohuh fishuhnt) noun Mathematics → derivative (def. 7a) …  

  • differential — dif fer*en tial, a. [Cf. F. diff[ e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster] For whom he… …   The Collaborative International Dictionary of English

  • Differential calculus — differential dif fer*en tial, a. [Cf. F. diff[ e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster] For… …   The Collaborative International Dictionary of English

  • Differential coupling — differential dif fer*en tial, a. [Cf. F. diff[ e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster] For… …   The Collaborative International Dictionary of English

  • Differential duties — differential dif fer*en tial, a. [Cf. F. diff[ e]rentiel.] 1. Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate. [1913 Webster] For… …   The Collaborative International Dictionary of English

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