# 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.

### 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 ...
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 given by That is, the slope of the ... 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 ...
Aesculetin
... Aesculetin (also known as esculetin, 6,7-dihydroxycoumarin and cichorigenin) is a derivative of coumarin ... cyclization of a cinnamic acid derivative ... The sodium salt of its methyl-derivative is used in dermatology for the treatment of varicose veins ...
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 ... It remains to show that this representation of the derivative implies Liouville's formula ... both sides, using the product rule, the chain rule, the derivative of the exponential function and the fundamental theorem of calculus, we obtain ...
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 ... For example one 2,3-diarylpyridine derivative was shown to be potent and selective CB1 inverse agonist ...

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When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science the vulgarized derivative from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.
Wyndham Lewis (1882–1957)