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  2. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    The rule for integration by parts is derived from the product rule, as is (a weak version of) the quotient rule. (It is a "weak" version in that it does not prove that the quotient is differentiable but only says what its derivative is if it is differentiable.)

  3. Rule of product - Wikipedia

    en.wikipedia.org/wiki/Rule_of_product

    In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. [1] [2]

  4. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.

  5. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts can be extended to functions of several variables by applying a version of the fundamental theorem of calculus to an appropriate product rule. There are several such pairings possible in multivariate calculus, involving a scalar-valued function u and vector-valued function (vector field) V .

  6. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    In mathematics, the Lambert W function, also called the omega function or product logarithm, [1] is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function. The function is named after Johann Lambert, who considered a related problem in 1758.

  7. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    The convolution defines a product on the linear space of integrable functions. This product satisfies the following algebraic properties, which formally mean that the space of integrable functions with the product given by convolution is a commutative associative algebra without identity (Strichartz 1994, §3.3).

  8. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    By expanding the product on the left-hand side, equation follows. To prove the inclusion–exclusion principle for the cardinality of sets, sum the equation over all x in the union of A 1, ..., A n. To derive the version used in probability, take the expectation in . In general, integrate the equation with respect to μ. Always use linearity in ...

  9. Outer product - Wikipedia

    en.wikipedia.org/wiki/Outer_product

    If the two coordinate vectors have dimensions n and m, then their outer product is an n × m matrix. More generally, given two tensors (multidimensional arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their tensor product, and can be used to define the tensor algebra.