Derivaattien

Derivaatta is a Finnish term that translates to "derivative" in English, a fundamental concept in calculus. A derivative represents the instantaneous rate of change of a function with respect to one of its variables. Geometrically, it can be interpreted as the slope of the tangent line to the function's graph at a specific point. The process of finding a derivative is called differentiation. Derivatives are widely used in various fields, including physics, economics, and engineering, to model and analyze phenomena involving change. For example, in physics, the derivative of position with respect to time gives velocity, and the derivative of velocity with respect to time gives acceleration. In economics, derivatives can be used to analyze marginal cost and marginal revenue. The notation for a derivative of a function f(x) is often written as f'(x) or dy/dx. Higher-order derivatives, such as the second derivative (f''(x)), represent rates of change of the rate of change, providing information about concavity and acceleration. The concept of the limit is crucial for understanding and defining derivatives formally.