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人気のある微分積分 >

d/(dt)(e^{4(e^t-1)})

解

\frac{d}{d t} (e^{4 (e^{t} - 1)})

解

4 e^{4 (e^{t} - 1) + t}

解答ステップ

\frac{d}{d t} (e^{4 (e^{t} - 1)})

連鎖法則を適用:

e^{4 (e^{t} - 1)} \frac{d}{d t} (4 (e^{t} - 1))

= e^{4 (e^{t} - 1)} \frac{d}{d t} (4 (e^{t} - 1))

\frac{d}{d t} (4 (e^{t} - 1)) = 4 e^{t}

= e^{4 (e^{t} - 1)} \cdot 4 e^{t}

指数の規則を適用する:

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

e^{4 (e^{t} - 1)} e^{t} = e^{4 (e^{t} - 1) + t}

= 4 e^{4 (e^{t} - 1) + t}

グラフ

人気の例

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