(\partial)/(\partial x)(e^{4(e^x-1)})

解

\frac{\partial}{\partial x} (e^{4 (e^{x} - 1)})

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

解答ステップ

\frac{\partial}{\partial x} (e^{4 (e^{x} - 1)})

連鎖法則を適用:

e^{4 (e^{x} - 1)} \frac{\partial}{\partial x} (4 (e^{x} - 1))

= e^{4 (e^{x} - 1)} \frac{\partial}{\partial x} (4 (e^{x} - 1))

\frac{\partial}{\partial x} (4 (e^{x} - 1)) = 4 e^{x}

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

指数の規則を適用する:

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

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

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