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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.
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' law may refer to: The product rule; General Leibniz rule, a generalization of the product rule; Identity of indiscernibles; See also. Leibniz (disambiguation)
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.
Leibniz's rule (named after Gottfried Wilhelm Leibniz) may refer to one of the following: Product rule in differential calculus; General Leibniz rule, ...
The test was devised 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]
Haig–Simons income or Schanz–Haig–Simons income is an income measure used by public finance economists to analyze economic well-being which defines income as consumption plus change in net worth. [1] [2] It is represented by the mathematical formula: I = C + ΔNW. where C = consumption and ΔNW = change in net worth.
Until A Theory of Consumption Function, the Keynesian absolute income hypothesis and interpretation of the consumption function were the most advanced and sophisticated. [2] [3] In its post-war synthesis, the Keynesian perspective was responsible for pioneering many innovations in recession management, economic history, and macroeconomics.