Lesson plan
Differential coefficient
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). 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 , 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. 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.
Article summary
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). 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 , 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. 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.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.