diffeentsiaalarvutuste

Diffeentsiaalarvutused, commonly known as differential calculus, is a branch of calculus concerned with the study of rates of change and the properties of functions. It focuses on how a function's value changes as its input changes. The central concept in differential calculus is the derivative, which mathematically represents the instantaneous rate of change of a function at a specific point.

The derivative of a function can be understood as the slope of the tangent line to the function's graph at that point. This concept has wide-ranging applications in physics, engineering, economics, and many other fields where understanding change is crucial. For instance, in physics, derivatives are used to describe velocity from position, acceleration from velocity, and forces from motion. In economics, they can model marginal cost and marginal revenue.

Key concepts within differential calculus include limits, continuity, and differentiation rules. Limits are fundamental to defining derivatives and understanding the behavior of functions as they approach certain values. Differentiation rules provide systematic methods for calculating derivatives of various types of functions, such as polynomial, trigonometric, exponential, and logarithmic functions. The process of finding a derivative is called differentiation.

The inverse operation of differentiation is integration, which is the domain of integral calculus. Together, differential and integral calculus form the foundation of calculus, a powerful mathematical tool that has revolutionized scientific and technological advancements.