Differential coefficient

In today's world, Differential coefficient has become a topic of great importance and interest to a wide variety of people. Whether due to its impact on society, its relevance in the professional field or its influence on popular culture, Differential coefficient has positioned itself as a fundamental point of reference today. As time progresses, the importance of Differential coefficient continues to grow, making a detailed analysis of its various facets and its relevance in different contexts indispensable. In this article, we will thoroughly explore the meaning and implications of Differential coefficient, as well as its impact on different aspects of contemporary life.

In physics and 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).[1][2]

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 linear, its differential coefficient is a function, call it f′, derived by the differentiation of f, hence, the modern term, derivative.

The older usage is now rarely seen.

Early editions of Silvanus P. Thompson's Calculus Made Easy use the older term.[3] In his 1998 update of this text, 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.

References

  1. ^ Wansbrough, William Dyson (1912). The ABC of the Differential Calculus (3rd ed.). London: The Technical Publishing Company.
  2. ^ De Morgan, Augustus (April 2007) . Differential and Integral Calculus. New York: Cosimo. ISBN 9781602063792.
  3. ^ Thompson, Silvanus P. (October 1914). Calculus Made Easy (second, enlarged ed.). New York: The Macmillan Company. p. 15.