deriváltként

In mathematics, "deriváltként" is the Hungarian term for "as a derivative." It refers to the concept of a derivative, which is a fundamental tool in calculus. The derivative of a function measures the rate at which the function's value changes with respect to its input. Geometrically, it represents the slope of the tangent line to the function's graph at a particular point.

The process of finding a derivative is called differentiation. It can be understood through the limit definition: the derivative of a function f(x) at a point x is the limit of the difference quotient as the change in x approaches zero. This is expressed as lim (h->0) [f(x+h) - f(x)] / h.

Derivatives have widespread applications in various fields. In physics, they are used to describe velocity and acceleration. In economics, they help analyze marginal cost and revenue. Optimization problems, where one seeks to find maximum or minimum values of a function, heavily rely on derivative calculations. The existence and value of a derivative at a point indicate the smoothness and instantaneous rate of change of the function at that point. Functions that are differentiable at a point are also continuous at that point, but the converse is not always true.