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 "product rule, product, rule, rules, products":

*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 ... 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**- Applications - Definition of Tangent Space

...

**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 ...

**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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