Differenciálási

Differenciálási is a term used in mathematics, specifically within calculus, to refer to the process of finding the derivative of a function. The derivative of a function at a particular point represents the instantaneous rate of change of the function's value with respect to its input variable. Geometrically, the derivative at a point corresponds to the slope of the tangent line to the function's graph at that point.

The fundamental concept behind differenciálási involves examining how a function's output changes as its input changes by an infinitesimally small amount. This is often expressed using limits. The derivative of a function f(x) with respect to x is commonly denoted as f'(x), dy/dx, or D_x f(x).

There are established rules and techniques for performing differenciálási, such as the power rule, product rule, quotient rule, and chain rule, which allow for the differentiation of various types of functions. Differenciálási has broad applications in fields like physics (e.g., velocity and acceleration), economics (e.g., marginal cost and revenue), engineering, and computer science, enabling the analysis and modeling of dynamic systems and optimization problems. The inverse operation of differenciálási is integration, which deals with finding antiderivatives or areas under curves.