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人気のある微分積分 >

derivative of e^{e^{e^x}}

解

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

解

e^{e^{e^{x}} + e^{x} + x}

解答ステップ

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

連鎖法則を適用:

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

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

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

= e^{e^{e^{x}}} e^{e^{x} + x}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{e^{x}}} e^{e^{x} + x} = e^{e^{e^{x}} + e^{x} + x}

= e^{e^{e^{x}} + e^{x} + x}

グラフ

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