Product Rule

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:


Read more about Product Rule:  Discovery By Leibniz, Examples, A Common Error, Proof of The Product Rule, Applications

Other articles related to "rule, rules, product rule, product":

Properties of Hyperdeterminants - Multiplicative 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 ... The full domain of cases in which the product rule can be generalized is still a subject of research ...
Product Rule - Applications - Definition of Tangent Space
... Product rule is also used in definition of abstract tangent space of some abstract geometric figure (smooth manifold) ... functions on that 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 tangent space ...
Mathematical Induction - Variants - Building On n = 2 - Example: Product Rule For The Derivative
... 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 ... the n = 0 case is trivial, (since the empty product is 1, and the empty sum is 0) ... lies in the n = 2 case, which is why that is the one stated in the standard product rule ...
Geometric Calculus - Differentiation - Product Rule
... 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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