chain rule

Noun

Meaning

chain rule

(calculus) A formula for computing the derivative of the functional composition of two or more functions.

Synonyms

Examples

Higher derivatives Faà di Bruno's formula generalizes the chain rule to higher derivatives. Source: Internet

By applying the chain rule, the last expression becomes: : which is the usual formula for the quotient rule. Source: Internet

Composites of more than two functions The chain rule can be applied to composites of more than two functions. Source: Internet

From this perspective the chain rule therefore says: : or for short, : That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points). Source: Internet

In this case, the above rule for Jacobian matrices is usually written as: : The chain rule for total derivatives implies a chain rule for partial derivatives. Source: Internet

It also makes the chain rule easy to remember:In the formulation of calculus in terms of limits, the du symbol has been assigned various meanings by various authors. Source: Internet

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