在新选项卡中打开链接
  1. Wikipedia
    https://en.wikipedia.org › wiki › Product_rule

    Product rule - Wikipedia

    • In abstract algebra, the product rule is the defining property of a derivation. In this terminology, the product rule states that the derivative operator is a derivation on functions. 展开

    Overview

    In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of … 展开

    Discovery

    Discovery of this rule is credited to Gottfried Leibniz, who demonstrated it using "infinitesimals" (a precursor to the modern differential). (However, J. M. Child, a translator of Leibniz's papers, argues that it is due to … 展开

    Proofs

    Let h(x) = f(x)g(x) and suppose that f and g are each differentiable at x. We want to prove that h is differentiable at x and that its derivative, h′(x), is given by f′(x)g(x) + f(x)g′(x). To do this, (which is zero, and thus does not chang… 展开

    Generalizations

    The product rule can be generalized to products of more than two factors. For example, for three factors we have For a collection of functions , we have
    The logarithmic derivative provides a simpler expression of th… 展开

    Applications

    Among the applications of the product rule is a proof that when n is a positive integer (this rule is true even if n is not positive or is not an integer, but the proof of that must rely on other methods). The proof is by mathematical ind… 展开

    CC-BY-SA 许可证中的维基百科文本
    反馈

  1. Why Is There a Product Rule for Differentiation 的相关搜索

  2. 某些结果已被删除