differensial

Differensial is a term used in Danish, Norwegian and related languages to denote related ideas in mathematics and engineering. In mathematics, it refers to an infinitesimal change in a variable or to a linear approximation of a function’s change. For a differentiable function f of one variable, the differential df is f′(x) dx; for a function of several variables, df = ∑ ∂f/∂x_i dx_i. Differentials underpin differential calculus, the chain rule, and methods of integration such as substitution and the use of differential forms.

In a broader sense, the concept appears in differential equations, equations that relate a function to its derivatives. A first‑order ODE, dy/dx = g(x,y), describes how the unknown function y(x) evolves when x changes, subject to initial conditions.

In engineering, differensial (differential) denotes a mechanical gear train at a vehicle’s driveline. Its primary purpose is to split torque between the wheels on an axle and to allow them to rotate at different speeds, which is necessary when cornering. Common variants include open differentials, limited‑slip types, and locking differentials, each offering different balance between traction and handling.

Origin and usage: the term stems from Latin differentia; in many languages, including Danish and Norwegian, differensial is used interchangeably with differential depending on region and context.