afleiðujreikningur

Afleiðujreikningur, a term originating from Icelandic, translates to "derivative calculation" or "differential calculus" in English. It is a fundamental branch of calculus that deals with the rates of change of quantities. The core concept is the derivative, which measures how a function's output changes with respect to a small change in its input.

Geometrically, the derivative of a function at a particular point represents the slope of the tangent line to the function's graph at that point. This provides a way to understand the instantaneous rate of change of a dynamic system. For instance, if a function describes the position of an object over time, its derivative would represent the object's instantaneous velocity.

The process of finding a derivative is called differentiation. This can be done using a set of rules, such as the power rule, product rule, quotient rule, and chain rule, which simplify the calculation for various types of functions. Differentiation is crucial in numerous scientific and engineering disciplines, including physics, economics, and computer science, for modeling and analyzing changing phenomena.