Derivaattinen

Derivaatta is a Finnish term that translates to "derivative" in English, a fundamental concept in calculus. It represents the instantaneous rate of change of a function with respect to its variables. Geometrically, the derivative of a function at a particular point corresponds to the slope of the tangent line to the function's graph at that point. The process of finding a derivative is called differentiation.

The derivative is denoted in various ways, commonly as f'(x) for a function f(x), or dy/dx, indicating the change in y with respect to the change in x. Derivatives are crucial for understanding concepts like velocity and acceleration in physics, optimization problems in mathematics and economics, and the behavior of functions, such as identifying where they are increasing or decreasing. The existence of a derivative at a point implies that the function is differentiable at that point, meaning its graph is smooth and does not have sharp corners or breaks.