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The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.
The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion. The test is only sufficient, not necessary, so some convergent alternating series may fail the first part of the test. [1] [2] [3] For a generalization, see Dirichlet's test. [4] [5] [6]
Print/export Download as PDF; Printable version; In other projects ... General Leibniz rule, a generalization of the product rule; Identity of indiscernibles; See also
In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.For two functions, it may be stated in Lagrange's notation as () ′ = ′ + ′ or in Leibniz's notation as () = +.
Leibniz's rule (named after Gottfried Wilhelm Leibniz) may refer to one of the following: Product rule in differential calculus; General Leibniz rule, a generalization of the product rule; Leibniz integral rule; The alternating series test, also called Leibniz's rule
English: This is an illustration used to go with a proof of Leibniz's product rule in differential calculus, which I'm intending to add to the "Product rule" article in en.wikipedia Date 24 December 2012
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Leibniz theorem (named after Gottfried Wilhelm Leibniz) may refer to one of the following: Product rule in differential calculus; General Leibniz rule, a generalization of the product rule; Leibniz integral rule; The alternating series test, also called Leibniz's rule; The Fundamental theorem of calculus, also called Newton-Leibniz theorem.