derivácii

Derivácii is a concept in mathematics that refers to the rate at which a function changes as its input changes. It is a fundamental concept in calculus, a branch of mathematics that deals with rates of change and accumulation of quantities. The derivative of a function at a given point is the slope of the tangent line to the function's graph at that point. This slope represents the instantaneous rate of change of the function at that point.

The derivative of a function f(x) is denoted by f'(x) or df/dx. It can be computed using various methods, including the limit definition, which involves taking the limit of the difference quotient as the change in x approaches zero. Alternatively, derivatives can be found using differentiation rules, such as the power rule, product rule, and chain rule.

Derivatives have numerous applications in mathematics, physics, engineering, and other fields. They are used to find the velocity and acceleration of moving objects, to determine the maximum and minimum values of functions, and to solve optimization problems. In physics, derivatives are used to describe the rate of change of physical quantities, such as velocity and acceleration.

In summary, derivácii is a crucial concept in calculus that describes the rate at which a function changes. It is computed using various methods and has wide-ranging applications in mathematics, physics, and other fields.