Diferentsiatsiooni

Diferentsiatsiooni is a fundamental concept in mathematics, specifically within calculus. It refers to the process of finding the derivative of a function. The derivative of a function at a specific point represents the instantaneous rate of change of that function at that point, or geometrically, the slope of the tangent line to the function's graph at that point.

The operation of differentiation is denoted by various symbols, such as dy/dx, f'(x), or D_x f(x). The process involves applying differentiation rules to find the derivative function. These rules are derived from the limit definition of the derivative and include power rule, product rule, quotient rule, and chain rule, among others.

Differentiation has wide-ranging applications in various fields. In physics, it is used to describe velocity and acceleration, which are derivatives of position with respect to time. In economics, it helps in analyzing marginal cost and marginal revenue. In engineering, it is employed in optimization problems and the study of dynamic systems. Understanding differentiation is crucial for solving problems involving rates of change, optimization, and analyzing the behavior of functions.