Derivative

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.

The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function.

The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

Read more about DerivativeDifferentiation and The Derivative, Computing The Derivative, Generalizations

Other articles related to "derivative, derivatives":

Derivative - Generalizations
... The concept of a derivative can be extended to many other settings ... The common thread is that the derivative of a function at a point serves as a linear approximation of the function at that point ... An important generalization of the derivative concerns complex functions of complex variables, such as functions from (a domain in) the complex numbers C to C ...
Proof of Liouville's Formula
... By the Leibniz formula for determinants, the derivative of the determinant of Φ = (Φi, j )i, j ∈ {0...n} can be calculated by differentiating one row at a time and taking the sum, i.e (2) Since the ... It remains to show that this representation of the derivative implies Liouville's formula ... using the product rule, the chain rule, the derivative of the exponential function and the fundamental theorem of calculus, we obtain due to the derivative in (3) ...
Cannabinoid Receptor Antagonist - Drug Design - Other Derivatives
... A large number of fused bicyclic derivatives of diaryl-pyrazole and imidazoles have been reported ... An example of these is a purine derivative where a pyrimidine ring is fused to an imidazole ring ... Otenabant (CP-945,598) is an example of a fused bicyclic derivative developed by Pfizer ...
Aesculetin
... esculetin, 6,7-dihydroxycoumarin and cichorigenin) is a derivative of coumarin ... intramolecular cyclization of a cinnamic acid derivative ... The sodium salt of its methyl-derivative is used in dermatology for the treatment of varicose veins ...
Logrithm - Analytic Properties - Derivative and Antiderivative
... Moreover, as the derivative of f(x) evaluates to ln(b)bx by the properties of the exponential function, the chain rule implies that the derivative of logb(x) is ... In particular, the derivative of ln(x) is 1/x, which implies that the antiderivative of 1/x is ln(x) + C ... The derivative with a generalised functional argument f(x) is The quotient at the right hand side is called the logarithmic derivative of f ...

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