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  2. Chain rule - Wikipedia

    en.wikipedia.org/wiki/Chain_rule

    All extensions of calculus have a chain rule. In most of these, the formula remains the same, though the meaning of that formula may be vastly different. One generalization is to manifolds. In this situation, the chain rule represents the fact that the derivative of f ∘ g is the composite of the derivative of f and the derivative of g. This ...

  3. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    chain rule The chain rule is a formula for computing the derivative of the composition of two or more functions. That is, if f and g are functions, then the chain rule expresses the derivative of their composition f ∘ g (the function which maps x to f(g(x)) ) in terms of the derivatives of f and g and the product of functions as follows:

  4. List of calculus topics - Wikipedia

    en.wikipedia.org/wiki/List_of_calculus_topics

    Power rule; Chain rule; Local linearization; Product rule; Quotient rule; Inverse functions and differentiation; Implicit differentiation; Stationary point. Maxima and minima; First derivative test; Second derivative test; Extreme value theorem; Differential equation; Differential operator; Newton's method; Taylor's theorem; L'Hôpital's rule ...

  5. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    The product rule and chain rule, [25] the notions of higher derivatives and Taylor series, [26] and of analytic functions [27] were used by Isaac Newton in an idiosyncratic notation which he applied to solve problems of mathematical physics. In his works, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing ...

  6. Geometric calculus - Wikipedia

    en.wikipedia.org/wiki/Geometric_calculus

    In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to reproduce other mathematical theories including vector calculus , differential geometry , and differential forms .

  7. Integration by substitution - Wikipedia

    en.wikipedia.org/wiki/Integration_by_substitution

    In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."

  8. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. [23] Analytic geometry allows the study of curves unrelated to circles and lines.

  9. Itô's lemma - Wikipedia

    en.wikipedia.org/wiki/Itô's_lemma

    In mathematics, Itô's lemma or Itô's formula is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process.It serves as the stochastic calculus counterpart of the chain rule.

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