Chain rule: Difference between revisions
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imported>Richard Pinch (new entry, just a stub, needs examples, multilinear version and theorem) |
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Revision as of 02:45, 8 November 2008
In calculus, the chain rule describes the derivative of a "function of a function": the composition of two function, where the output z is a given function of an intermediate variable y which is in turn a given function of the input variable x.
Suppose that y is given as a function and that z is given as a function . The rate at which z varies in terms of y is given by the derivative , and the rate at which y varies in terms of x is given by the derivative . So the rate at which z varies in terms of x is the product , and substituting we have the chain rule
In traditional "d" notation we write