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  2. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    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 () = +.

  3. File:Triangle diagram of rewrite rule application.pdf - Wikipedia

    en.wikipedia.org/wiki/File:Triangle_diagram_of...

    Original file (1,068 × 489 pixels, file size: 13 KB, MIME type: application/pdf) This is a file from the Wikimedia Commons . Information from its description page there is shown below.

  4. Triple product rule - Wikipedia

    en.wikipedia.org/wiki/Triple_product_rule

    Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...

  5. General Leibniz rule - Wikipedia

    en.wikipedia.org/wiki/General_Leibniz_rule

    The Leibniz rule bears a strong resemblance to the binomial theorem, and in fact the binomial theorem can be proven directly from the Leibniz rule by taking () = and () =, which gives ( a + b ) n e ( a + b ) x = e ( a + b ) x ∑ k = 0 n ( n k ) a n − k b k , {\displaystyle (a+b)^{n}e^{(a+b)x}=e^{(a+b)x}\sum _{k=0}^{n}{\binom {n}{k}}a^{n-k}b ...

  6. Secretary problem - Wikipedia

    en.wikipedia.org/wiki/Secretary_problem

    Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory.

  7. Rule of product - Wikipedia

    en.wikipedia.org/wiki/Rule_of_product

    In this example, the rule says: multiply 3 by 2, getting 6. The sets {A, B, C} and {X, Y} in this example are disjoint sets, but that is not necessary.The number of ways to choose a member of {A, B, C}, and then to do so again, in effect choosing an ordered pair each of whose components are in {A, B, C}, is 3 × 3 = 9.

  8. Reciprocal rule - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_rule

    Also, one can readily deduce the quotient rule from the reciprocal rule and the product rule. The reciprocal rule states that if f is differentiable at a point x and f(x) ≠ 0 then g(x) = 1/f(x) is also differentiable at x and ′ = ′ ().

  9. Multiple rule-based problems - Wikipedia

    en.wikipedia.org/wiki/Multiple_rule-based_problems

    Multiple rule-based problems are problems containing various conflicting rules and restrictions. [1] Such problems typically have an " optimal " solution, found by striking a balance between the various restrictions, without directly defying any of the aforementioned restrictions.

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