Deriváty

Derivát, deriváty, is a Czech term with several related meanings in different scientific contexts, most notably in mathematics and chemistry. In mathematics, derivát refers to the derivative of a function at a point. It is defined as the limit of the difference quotient as the increment approaches zero and is commonly denoted f′(x) or dy/dx. The derivative represents the instantaneous rate of change of the function and has a geometric interpretation as the slope of the tangent line to the graph at a given point. Derivatives of higher order, such as f′′(x), describe rates of change of the rate of change and underpin many applications in physics, engineering, and economics.

In chemistry, a derivát is a compound derived from a parent compound by chemical modification, such as substitution or the addition of a functional group. Deriváty are used to study structure, reactivity, or to facilitate analysis. The process of creating derivatives, derivatizace, is common in analytical chemistry to improve detection, separation, or stability of compounds. Examples include acetyl derivatives, methyl derivatives, and various halogen or nitro derivatives, all of which help in characterization and analysis.

Etymology-wise, derivát comes from Latin derivatus, adapted through Czech. The term is used in both scientific languages, but its meaning differs by context: in mathematics it denotes a rate of change of a function, while in chemistry it denotes a compound derived from another by modification.