Difference between revisions of "Chain rule"

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In [[calculus]], the '''chain rule''' describes the [[derivative]] of a "function of a function": the [[composition (mathematics)|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''.
 
In [[calculus]], the '''chain rule''' describes the [[derivative]] of a "function of a function": the [[composition (mathematics)|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''.
  

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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

See also