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Derivative

Index Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). [1]

147 relations: Absolute value, Acceleration, Almost everywhere, Antiderivative, Approximation, Arc length, Arithmetic derivative, Automatic differentiation, , Banach space, Calculus, Calculus Made Easy, Cauchy–Riemann equations, Chain rule, Complex number, Complex-valued function, Concave function, Constant function, Continuous function, Convex function, Currying, Delta (letter), Dependent and independent variables, Derivative, Diagonal functor, Difference quotient, Differentiable function, Differentiable manifold, Differential (infinitesimal), Differential algebra, Differential equation, Differential geometry, Differential geometry of curves, Differential geometry of surfaces, Differential operator, Differentiation rules, Differintegral, Dimension (vector space), Dirac measure, Distribution (mathematics), Division by zero, Domain of a function, Equality (mathematics), Euclidean vector, Exponential function, Exterior derivative, Finite difference, Fractal derivative, Fréchet derivative, Fréchet space, ..., Function (mathematics), Function of a real variable, Function of several real variables, Fundamental theorem of calculus, Gâteaux derivative, Generalizations of the derivative, Gottfried Wilhelm Leibniz, Gradient, Graph of a function, Hasse derivative, History of calculus, Holomorphic function, Hyperreal number, Infinitesimal, Integral, Inverse trigonometric functions, Isaac Newton, Jacobian matrix and determinant, Jerk (physics), Jet (mathematics), Jet bundle, Joseph-Louis Lagrange, Jounce, Keith Stroyan, Khan Academy, Leibniz's notation, Leibniz–Newton calculus controversy, Leonhard Euler, Limit (mathematics), Limit of a function, Linear approximation, Linear differential equation, Linear function, Linear map, Linearity, Linearity of differentiation, Linearization, Lipschitz continuity, Logarithm, Mathematical analysis, Mathematics, Matrix (mathematics), Meagre set, Monotonic function, Multiplicative inverse, Necessity and sufficiency, Neighbourhood (mathematics), Non-standard analysis, Norm (mathematics), Notation for differentiation, Numerical differentiation, Operator (mathematics), Parametric equation, Partial derivative, Physics, Polynomial, Power rule, Prime (symbol), Product rule, Pullback (differential geometry), Pushforward (differential), Quotient rule, Radon–Nikodym theorem, Rate (mathematics), Real number, Real-valued function, Scalar field, Schwarzian derivative, Secant line, Second derivative, Series (mathematics), Slope, Smoothness, Standard part function, Stefan Banach, Step function, Subscript and superscript, Symmetric derivative, Tangent, Tangent bundle, Tangent space, Taylor series, Third derivative, Time, Time-scale calculus, Total derivative, Transversality (mathematics), Trigonometric functions, University of Minnesota, Vector field, Vector space, Vector-valued function, Velocity, Vertical tangent, Weak derivative, Weierstrass function, Wolfram Alpha. Expand index (97 more) »

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Acceleration

In physics, acceleration is the rate of change of velocity of an object with respect to time.

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Almost everywhere

In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.

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Antiderivative

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.

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Approximation

An approximation is anything that is similar but not exactly equal to something else.

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Arc length

Determining the length of an irregular arc segment is also called rectification of a curve.

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Arithmetic derivative

In number theory, the Lagarias arithmetic derivative, or number derivative, is a function defined for integers, based on prime factorization, by analogy with the product rule for the derivative of a function that is used in mathematical analysis.

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Automatic differentiation

In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program.

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The character ∂ (HTML element: ∂ or ∂, Unicode: U+2202) or \partial is a stylized d mainly used as a mathematical symbol to denote a partial derivative such as \frac (read as "the partial derivative of z with respect to x").

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Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Calculus Made Easy

Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson.

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Cauchy–Riemann equations

In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.

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Chain rule

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Complex-valued function

In mathematics, a complex-valued function (not to be confused with complex variable function) is a function whose values are complex numbers.

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Concave function

In mathematics, a concave function is the negative of a convex function.

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Constant function

In mathematics, a constant function is a function whose (output) value is the same for every input value.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Currying

In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments (or a tuple of arguments) into evaluating a sequence of functions, each with a single argument.

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Delta (letter)

Delta (uppercase Δ, lowercase δ or 𝛿; δέλτα délta) is the fourth letter of the Greek alphabet.

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Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Diagonal functor

In category theory, a branch of mathematics, the diagonal functor \mathcal \rightarrow \mathcal \times \mathcal is given by \Delta(a).

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Difference quotient

In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x+h)-x.

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

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Differential (infinitesimal)

The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity.

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Differential algebra

In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Differential geometry of curves

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus.

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Differential geometry of surfaces

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.

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Differential operator

In mathematics, a differential operator is an operator defined as a function of the differentiation operator.

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Differentiation rules

This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.

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Differintegral

In fractional calculus, an area of applied mathematics, the differintegral is a combined differentiation/integration operator.

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Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

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Dirac measure

In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed element x or not.

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Distribution (mathematics)

Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.

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Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Exterior derivative

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.

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Finite difference

A finite difference is a mathematical expression of the form.

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Fractal derivative

In applied mathematics and mathematical analysis, the fractal derivative is a nonstandard type of derivative in which the variable such as t has been scaled according to tα.

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Fréchet derivative

In mathematics, the Fréchet derivative is a derivative defined on Banach spaces.

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Fréchet space

In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Function of a real variable

In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers, or a subset of that contains an interval of positive length.

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Function of several real variables

In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables.

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Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.

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Gâteaux derivative

In mathematics, the Gâteaux differential or Gâteaux derivative is a generalization of the concept of directional derivative in differential calculus.

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Generalizations of the derivative

In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Hasse derivative

In mathematics, the Hasse derivative is a generalisation of the derivative which allows the formulation of Taylor's theorem in coordinate rings of algebraic varieties.

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History of calculus

Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series.

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

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Hyperreal number

The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.

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Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Inverse trigonometric functions

In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

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Jerk (physics)

In physics, jerk is the rate of change of acceleration; that is, the time derivative of acceleration, and as such the second derivative of velocity, or the third time derivative of position.

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Jet (mathematics)

In mathematics, the jet is an operation that takes a differentiable function f and produces a polynomial, the truncated Taylor polynomial of f, at each point of its domain.

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Jet bundle

In differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Jounce

In physics, jounce, also known as snap, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time.

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Keith Stroyan

Keith D. Stroyan is Professor of Mathematics at the University of Iowa.

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Khan Academy

Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with a goal of creating a set of online tools that help educate students.

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Leibniz's notation

dydx d2ydx2 In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols and to represent infinitely small (or infinitesimal) increments of and, respectively, just as and represent finite increments of and, respectively.

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Leibniz–Newton calculus controversy

The calculus controversy (often referred to with the German term Prioritätsstreit, meaning "priority dispute") was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates) over who had first invented the mathematical study of change, calculus.

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Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

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Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

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Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

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Linear approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).

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Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.

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Linear function

In mathematics, the term linear function refers to two distinct but related notions.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Linearity

Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.

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Linearity of differentiation

In calculus, the derivative of any linear combination of functions equals the same linear combination of the derivatives of the functions; this property is known as linearity of differentiation, the rule of linearity, or the superposition rule for differentiation.

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Linearization

In mathematics, linearization is finding the linear approximation to a function at a given point.

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Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Meagre set

In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense small or negligible.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

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Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

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Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Notation for differentiation

In differential calculus, there is no single uniform notation for differentiation.

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Numerical differentiation

In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

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Operator (mathematics)

In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.

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Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Power rule

In calculus, the power rule is used to differentiate functions of the form f(x).

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Prime (symbol)

The prime symbol (′), double prime symbol (&Prime), triple prime symbol (&#x2034), quadruple prime symbol (&#x2057) etc., are used to designate units and for other purposes in mathematics, the sciences, linguistics and music.

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Product rule

In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.

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Pullback (differential geometry)

Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*.

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Pushforward (differential)

Suppose that is a smooth map between smooth manifolds; then the differential of φ at a point x is, in some sense, the best linear approximation of φ near x. It can be viewed as a generalization of the total derivative of ordinary calculus.

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Quotient rule

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions.

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Radon–Nikodym theorem

In mathematics, the Radon–Nikodym theorem is a result in measure theory.

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Rate (mathematics)

In mathematics, a rate is the ratio between two related quantities.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Real-valued function

In mathematics, a real-valued function is a function whose values are real numbers.

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Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.

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Schwarzian derivative

In mathematics, the Schwarzian derivative, named after the German mathematician Hermann Schwarz, is a certain operator that is invariant under all linear fractional transformations.

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Secant line

In geometry, a secant of a curve is a line that intersects the curve in at least two (distinct) points.

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Second derivative

In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of.

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Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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Smoothness

In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

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Standard part function

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers.

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Stefan Banach

Stefan Banach (30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians.

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Step function

In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals.

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Subscript and superscript

A subscript or superscript is a character (number, letter or symbol) that is (respectively) set slightly below or above the normal line of type.

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Symmetric derivative

In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative.

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Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Tangent bundle

In differential geometry, the tangent bundle of a differentiable manifold M is a manifold TM which assembles all the tangent vectors in M. As a set, it is given by the disjoint unionThe disjoint union ensures that for any two points x1 and x2 of manifold M the tangent spaces T1 and T2 have no common vector.

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Tangent space

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Third derivative

In calculus, a branch of mathematics, the third derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing, used to define aberrancy.

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Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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Time-scale calculus

In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid discrete–continuous dynamical systems.

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Total derivative

In the mathematical field of differential calculus, a total derivative or full derivative of a function f of several variables, e.g., t, x, y, etc., with respect to an exogenous argument, e.g., t, is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

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Transversality (mathematics)

In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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University of Minnesota

The University of Minnesota, Twin Cities (often referred to as the University of Minnesota, Minnesota, the U of M, UMN, or simply the U) is a public research university in Minneapolis and Saint Paul, Minnesota.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Vector-valued function

A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

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Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

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Vertical tangent

In mathematics, particularly calculus, a vertical tangent is tangent line that is vertical.

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Weak derivative

In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L''p'' space \mathrm^1().

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Weierstrass function

In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.

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Wolfram Alpha

Wolfram Alpha (also styled WolframAlpha, and Wolfram|Alpha) is a computational knowledge engine or answer engine developed by Wolfram Alpha LLC, a subsidiary of Wolfram Research.

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References

[1] https://en.wikipedia.org/wiki/Derivative

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