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人気のある微分積分 >

derivative f(x)=arccos(e^x)

解

導関数

f (x) = arccos (e^{x})

解

- \frac{e ^{x}}{1 - e ^{2 x}}

解答ステップ

\frac{d}{d x} (arccos (e^{x}))

連鎖法則を適用:

- \frac{1}{1 - ( e ^{x} ) ^{2}} \frac{d}{d x} (e^{x})

= - \frac{1}{1 - ( e ^{x} ) ^{2}} \frac{d}{d x} (e^{x})

\frac{d}{d x} (e^{x}) = e^{x}

= - \frac{1}{1 - ( e ^{x} ) ^{2}} e^{x}

簡素化

- \frac{1}{1 - ( e ^{x} ) ^{2}} e^{x} : - \frac{e ^{x}}{1 - e ^{2 x}}

= - \frac{e ^{x}}{1 - e ^{2 x}}

グラフ

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