Original: 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).
Simplified: In mathematics, 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).