In calculus, the product rule is a formula used to find the derivatives of products of two or more functions. It may be stated thus:
or in the Leibniz notation thus:
In the notation of differentials this can be written as follows:
The derivative of the product of three functions is:
Other articles related to "product rule, product, rule, rules, products":
... The usual product rule for the derivative taught in calculus states or in logarithmic derivative form This can be generalized to a product of n functions ... general fact is proved by mathematical induction, the n = 0 case is trivial, (since the empty product is 1, and the empty sum is 0) ... real difficulty lies in the n = 2 case, which is why that is the one stated in the standard product rule ...
... One of the most familiar properties of determinants is the multiplication rule which is sometimes known as the Binet-Cauchy formula ... For square n × n matrices A and B the rule says that det(AB) = det(A) det(B) This is one of the harder rules to generalize from determinants to hyperdeterminants because generalizations of products of ... The full domain of cases in which the product rule can be generalized is still a subject of research ...
... Product rule is also used in definition of abstract tangent space of some abstract geometric figure (smooth manifold) ... geometric figure at a point p solely with the product rule and that the set of all such derivations in fact forms a vector space that is the desired ...
... Although the partial derivative exhibits a product rule, the geometric derivative only partially inherits this property ... Consider two functions F and G Since the geometric product is not commutative with in general, we cannot proceed further without new notation ... In this case, if we define then the product rule for the geometric derivative is ...
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