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In mathematics, differential coefficient is a term out of use now. The former differential coefficient of a function f(x) is now called its derivative df(x)/dx. It is the (not necessarily constant) multiplicative factor or coefficient of the differential dx in the differential df(x).
Early editions of Silvanus P. Thompson's Calculus Made Easy use the older term. In his 1998 update of this text, Martin Gardner puts "derivative" instead of "differential coefficient". He speaks of it only in context with Thompson's criticism of the term.