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人気のある微分積分 >

derivative of e^{1/x}-1

解

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

解

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (1) = 0

= - \frac{e ^{\frac{1}{x}}}{x ^{2}} - 0

簡素化

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

グラフ

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