As such, it is used extensively in the back office during the design or maintenance of product rules.

The third line was obtained by use of a product rule for divergence.

The previous relation (where we have used the appropriate product rule) is known as the continuity equation.

This can be proved by using the product rule and mathematical induction.

In that case the more complicated proof of the product rule applies.

This follows from the product rule since the derivative of any constant is zero.

The product rule can be considered a special case of the chain rule for several variables.

The product rule can be generalized to products of more than two factors.

Again the power of the notation is shown by the product rule:

The full domain of cases in which the product rule can be generalized is still a subject of research.