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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 () = +.
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 logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): () ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.
2.3 Product rule for multiplication by a scalar. 2.4 Quotient rule for division by a scalar. ... Similar rules apply to algebraic and differentiation formulas. For ...
Product rule – Formula for the derivative of a product Reciprocal rule – differentiation rule Pages displaying wikidata descriptions as a fallback Table of derivatives – Rules for computing derivatives of functions Pages displaying short descriptions of redirect targets
The discrete equivalent of differentiation is finite differences. The study of differential calculus is unified with the calculus of finite differences in time scale calculus. [55] The arithmetic derivative involves the function that is defined for the integers by the prime factorization. This is an analogy with the product rule. [56]
Product rule: For two differentiable functions f and g, () = +. An operation d with these two properties is known in abstract algebra as a derivation . They imply the power rule d ( f n ) = n f n − 1 d f {\displaystyle d(f^{n})=nf^{n-1}df} In addition, various forms of the chain rule hold, in increasing level of generality: [ 12 ]
Differentiation rules – Rules for computing derivatives of functions; Exact differential – Type of infinitesimal in calculus (has another derivation of the triple product rule) Product rule – Formula for the derivative of a product; Total derivative – Type of derivative in mathematics