Differenzial

Differenzial is a term used in German that corresponds to the English "differential" and can refer to two distinct concepts: a mathematical notion used in calculus and a component of vehicle drivetrains in automotive engineering.

In mathematics, a differential denotes an infinitesimal change in a variable. For a function y = f(x), the differential dy is defined as f'(x) dx, where dx is an infinitesimal change in x. Differentials are central to differential calculus, where they express linear approximations to changes in y, appear in integration as part of the substitution and integration by parts methods, and underpin the formalism of differential forms in higher mathematics.

In automotive engineering, a mechanical differential is a gear train that splits torque between two wheels on the same axle while allowing them to rotate at different speeds. This arrangement enables smooth turning, as the outer wheel travels farther and faster than the inner wheel. A differential typically consists of bevel or hypoid gears, side gears, and spider gears within a differential housing. Common variants include open differentials, which evenly distribute torque but can lose traction if one wheel spins; limited-slip and locking differentials, which restrict speed or torque differences to improve grip; and center differentials in all-wheel-drive systems to balance torque between front and rear axles.

The term reflects historical and linguistic ties to Latin roots and is used in both mathematical and engineering contexts, with the German usage often paralleling the English term “differential.”