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  2. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    These rules are given in many books, both on elementary and advanced calculus, in pure and applied mathematics. Those in this article (in addition to the above references) can be found in: Mathematical Handbook of Formulas and Tables (3rd edition) , S. Lipschutz, M.R. Spiegel, J. Liu, Schaum's Outline Series, 2009, ISBN 978-0-07-154855-7 .

  3. Reciprocal rule - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_rule

    Chain rule – For derivatives of composed functions; Difference quotient – Expression in calculus; Differentiation of integrals – Problem in mathematics; Differentiation rulesRules for computing derivatives of functions; General Leibniz rule – Generalization of the product rule in calculus

  4. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to 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.

  5. Quotient rule - Wikipedia

    en.wikipedia.org/wiki/Quotient_rule

    Chain rule – For derivatives of composed functions; Differentiation of integrals – Problem in mathematics; Differentiation rulesRules for computing derivatives of functions; General Leibniz rule – Generalization of the product rule in calculus

  6. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    However, because integration is the inverse operation of differentiation, Lagrange's notation for higher order derivatives extends to integrals as well. Repeated integrals of f may be written as f ( − 1 ) ( x ) {\displaystyle f^{(-1)}(x)} for the first integral (this is easily confused with the inverse function f − 1 ( x ) {\displaystyle f ...

  7. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...

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