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In differential calculus, there is no single uniform notation for differentiation. Instead, several different notations for the derivative of a function or variable have been proposed by different mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context. The most common notations for differentiation are listed below. == Leibniz's notation == ''dy'' ''dx'' ''d''2''y'' ''dx''2 (詳細はGottfried Leibniz is used throughout mathematics. It is particularly common when the equation is regarded as a functional relationship between dependent and independent variables and . In this case the derivative can be written as: : The function whose value at is the derivative of at is therefore written : (although strictly speaking this denotes the variable value of the derivative function rather than the derivative function itself). Higher derivatives are expressed as : for the ''n''th derivative of ''y'' = ''f''(''x''). Historically, this came from the fact that, for example, the third derivative is: : which we can loosely write (dropping the brackets in the denominator) as: : as above. With Leibniz's notation, the value of the derivative of ''y'' at a point ''x'' = ''a'' can be written in two different ways: : Leibniz's notation allows one to specify the variable for differentiation (in the denominator). This is especially helpful when considering partial derivatives. It also makes the chain rule easy to remember and recognize: : In the formulation of calculus in terms of limits, the ''du'' symbol has been assigned various meanings by various authors. Some authors do not assign a meaning to ''du'' by itself, but only as part of the symbol ''du''/''dx''. Others define ''dx'' as an independent variable, and use ''d''(''x'' + ''y'') = ''dx'' + ''dy'' and ''d''(''x''·''y'') = ''dx''·''y'' + ''x''·''dy'' as formal axioms for differentiation. See differential algebra. In non-standard analysis ''du'' is defined as an infinitesimal. It is also interpreted as the exterior derivative d''u'' of a function ''u''. 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「Notation for differentiation」の詳細全文を読む スポンサード リンク
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