# Chain Rule

Also found in: Dictionary, Wikipedia.

Related to Chain Rule: implicit differentiation

## chain rule

[′chān ‚rül] (mathematics)

A rule for differentiating a composition of functions: (

*d/dx*) ƒ (*g*(*x*)) = ƒ′(*g*(*x*))·*g*′(*x*).## Chain Rule

a method given in old arithmetic textbooks for converting the measures of one system into the measures of another system by means of a third system.

Suppose, for example, we want to know the number of *vershki* equal to 3 feet if 1 foot is equal to 12 inches and 28 inches are equal to 16 *vershki*. To apply the chain rule, we write the elements of the problem in the following form:

x vershki | 3 feet |

1 foot | 12 inches |

28 inches | 16 vershki |

The required number of *vershki* is obtained by dividing the product of the numbers in the right-hand column by the product of the known numbers in the left-hand column: