“Chain Rule”的概念、定义、习题解题方法及翻译-数学辞典

单词

Chain Rule

释义

Chain Rule

If is Differentiable at the point and is Differentiable at the point , then is Differentiable at . Furthermore, let and , then

(1)

There are a number of related results which also go under the name of ``chain rules.'' For example, if

, and

, then

(2)

The ``general'' chain rule applies to two sets of functions


			(3)

and


			(4)

Defining the

Jacobi Matrix by

(5)

and similarly for

and

then gives

(6)

In differential form, this becomes

(7)

(Kaplan 1984).

See also Derivative, Jacobian, Power Rule, Product Rule

References

Anton, H. Calculus with Analytic Geometry, 2nd ed. New York: Wiley, p. 165, 1984.

Kaplan, W. ``Derivatives and Differentials of Composite Functions'' and ``The General Chain Rule.'' §2.8 and 2.9 in Advanced Calculus, 3rd ed. Reading, MA: Addison-Wesley, pp. 101-105 and 106-110, 1984.

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