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The differential was first introduced via an intuitive or heuristic definition by Isaac Newton and furthered by Gottfried Leibniz, who thought of the differential dy as an infinitely small (or infinitesimal) change in the value y of the function, corresponding to an infinitely small change dx in the function's argument x.
The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an ...
The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
A differential is a gear train with three drive shafts that has the property that the rotational speed of one shaft is the average of the speeds of the others. A common use of differentials is in motor vehicles , to allow the wheels at each end of a drive axle to rotate at different speeds while cornering.
This notation is sometimes called Euler's notation although it was introduced by Louis François Antoine Arbogast [8], and it seems that Leonhard Euler did not use it. [citation needed] This notation uses a differential operator denoted as D (D operator) [9] [failed verification] or D̃ (Newton–Leibniz operator). [10]
The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or ...
The differential operator del, also called nabla, is an important vector differential operator. It appears frequently in physics in places like the differential form of Maxwell's equations . In three-dimensional Cartesian coordinates , del is defined as
An exact differential is sometimes also called a total differential, or a full differential, or, in the study of differential geometry, it is termed an exact form. The integral of an exact differential over any integral path is path-independent, and this fact is used to identify state functions in thermodynamics.