|
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. That is, if ''f'' and ''g'' are functions, then the chain rule expresses the derivative of their composition (the function which maps ''x'' to ''f''(''g''(''x'')) in terms of the derivatives of ''f'' and ''g'' and the product of functions as follows: : This can be written more explicitly in terms of the variable. Let , or equivalently, for all ''x''. Then one can also write : The chain rule may be written, in Leibniz's notation, in the following way. We consider ''z'' to be a function of the variable ''y'', which is itself a function of ''x'' (''y'' and ''z'' are therefore dependent variables), and so, ''z'' becomes a function of ''x'' as well: : In integration, the counterpart to the chain rule is the substitution rule. == History == The chain rule seems to have first been used by Leibniz. He used it to calculate the derivative of as the composite of the square root function and the function . He first mentioned it in a 1676 memoir (with a sign error in the calculation). The common notation of chain rule is due to Leibniz. L'Hôpital uses the chain rule implicitly in his ''Analyse des infiniment petits''. The chain rule does not appear in any of Leonhard Euler's analysis books, even though they were written over a hundred years after Leibniz's discovery. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「chain rule」の詳細全文を読む スポンサード リンク
|