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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Differentiation of trigonometric functions ： ウィキペディア英語版 Differentiation of trigonometric functions } |- |$\backslash arccos(x)$ |$\backslash frac$ |} The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. Common trigonometric functions include sin(''x''), cos(''x'') and tan(''x''). For example, the derivative of ''f''(''x'') = sin(''x'') is represented as ''f'' ′(''a'') = cos(''a''). ''f'' ′(''a'') is the rate of change of sin(''x'') at a particular point ''a''. All derivatives of circular trigonometric functions can be found using those of sin(''x'') and cos(''x'') since they can all be expressed in terms of sine or cosine. The quotient rule is then implemented to differentiate the resulting expression. Finding the derivatives of the inverse trigonometric functions involves using implicit differentiation and the derivatives of regular trigonometric functions. ==Derivatives of trigonometric functions and their inverses== :$\backslash left(\backslash sin(x)\backslash right)\text{'}\; =\; \backslash cos(x)$ :$\backslash left(\backslash cos(x)\backslash right)\text{'}\; =\; -\backslash sin(x)$ :$\backslash left(\backslash tan(x)\backslash right)\text{'}\; =\; \backslash left(\backslash frac\backslash right)\text{'}\; =\; \backslash frac\; =\; 1\; +\; \backslash tan^2(x)\; =\; \backslash sec^2(x)$ :$\backslash left(\backslash cot(x)\backslash right)\text{'}\; =\; \backslash left(\backslash frac\backslash right)\text{'}\; =\; \backslash frac\; =\; -(1+\backslash cot^2(x))\; =\; -\backslash csc^2(x)$ :$\backslash left(\backslash sec(x)\backslash right)\text{'}\; =\; \backslash left(\backslash frac\backslash right)\text{'}\; =\; \backslash frac\; =\; \backslash frac\; \backslash cdot\; \backslash frac\; =\; \backslash sec(x)\backslash tan(x)$ :$\backslash left(\backslash csc(x)\backslash right)\text{'}\; =\; \backslash left(\backslash frac\backslash right)\text{'}\; =\; -\backslash frac\; =\; -\backslash frac\; \backslash cdot\; \backslash frac\; =\; -\backslash csc(x)\backslash cot(x)$ :$\backslash left(\backslash arcsin(x)\backslash right)\text{'}\; =\; \backslash frac$ :$\backslash left(\backslash operatorname\; (x)\backslash right)\text{'}\; =\; -\backslash frac$ :$\backslash left(\backslash operatorname\backslash \; (x)\backslash right)\text{'}\; =\; \backslash frac\backslash \; (x)\backslash right)\text{'}\; =\; -\backslash frac\{|x|\backslash sqrt\{x^2-1\}\}$ 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「Differentiation of trigonometric functions」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.