Noun
difference quotient (plural difference quotients)
(mathematical analysis) The slope of a secant as obtained by dividing the vertical difference between two intersections of the secant and a curve with their horizontal distance. When the horizontal distance approaches zero the slope of the secant approaches the derivative of the curve.
More directly, given a small change in x, the relative change in x is while the relative change in is Taking the ratio yields: : The last term is the difference quotient (the slope of the secant line), and taking the limit yields the derivative. Source: Internet
Consequently, the secant lines do not approach any single slope, so the limit of the difference quotient does not exist. Source: Internet
However, the usual difference quotient does not make sense in higher dimensions because it is not usually possible to divide vectors. Source: Internet
Rules of computation main The derivative of a function can, in principle, be computed from the definition by considering the difference quotient, and computing its limit. Source: Internet