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v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
This is a list of Latin words with derivatives in English (and other modern languages). Ancient orthography did not distinguish between i and j or between u and v. [1] Many modern works distinguish u from v but not i from j. In this article, both distinctions are shown as they are helpful when tracing the origin of English words.
f ′ ( x) A function f of x, differentiated once in Lagrange's notation. One of the most common modern notations for differentiation is named after Joseph Louis Lagrange, even though it was actually invented by Euler and just popularized by the former. In Lagrange's notation, a prime mark denotes a derivative.
Derivative (chemistry) In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction . In the past, derivative also meant a compound that can be imagined to arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, [ 1] but modern chemical language now ...
Derivatization. "Derivate" redirects here. For various senses of its synonym "derivative", see Derivative (disambiguation). Derivatization is a technique used in chemistry which converts a chemical compound into a product (the reaction's derivate) of similar chemical structure, called a derivative . Generally, a specific functional group of the ...
In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of ...
An ordinary differential equation ( ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y ), which, therefore, depends on x. Thus x is often called the independent variable of the equation.
A "derivative work" is a work based upon one or more preexisting works, such as a translation, musical arrangement, dramatization, fictionalization, motion picture version, sound recording, art reproduction, abridgment, condensation, or any other form in which a work may be recast, transformed, or adapted.