{{Unreferenced, date=June 2019, bot=noref (GreenC bot)
In physics, the differential coefficient of a function ''f''(''x'') is what is now called its
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
''df''(''x'')/''dx'', the (not necessarily constant) multiplicative factor or ''
coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves var ...
'' 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
In mathematics, the term linear function refers to two distinct but related notions:
* In calculus and related areas, a linear function is a function (mathematics), function whose graph of a function, graph is a straight line, that is, a polynomia ...
. 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
Silvanus Phillips Thompson (19 June 1851 – 12 June 1916) was a professor of physics at the City and Guilds Technical College in Finsbury, England. He was elected to the Royal Society in 1891 and was known for his work as an electrical eng ...
's ''
Calculus Made Easy
''Calculus Made Easy'' is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject. The original text continues to be available as of 2008 from Macmilla ...
'' use the older term. In his 1998 update of this text,
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...
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.
Mathematical analysis
Differential calculus
Functions and mappings