In calculus, the Leibniz notation, named in honor of the 17th century German philosopher and mathematician Gottfried Wilhelm Leibniz (pronounced LIPE nits) was originally the use of dx and dy and so forth to represent "infinitely small" increments of quantities x and y, just as Δx and Δy represent finite increments of x and y respectively. According to Leibniz, the derivative of y with resepct to x, which mathematicians later came to view as
Nonetheless, everyone continues to use Leibniz's notation today, and few doubt its utility in certain contexts. Although most people using it do not construe it literally, they find it simpler than alternatives when the technique of separation of variables is used in the solution of differential equations. In physical applications, one may for example regard f(x) as measured in meters per second, and dx in seconds, so that f(x) dx is in meters, and so is the value of its definite integral. In that way the Leibniz notation is in harmony with dimensional analysis.