derivative of e^{(e^{x^2}})

解

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

2 e^{e^{x^{2}} + x^{2}} x

解答ステップ

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

連鎖法則を適用:

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

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

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

= e^{e^{x^{2}}} e^{x^{2}} \cdot 2 x

指数の規則を適用する:

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

e^{e^{x^{2}}} e^{x^{2}} = e^{e^{x^{2}} + x^{2}}

= 2 e^{e^{x^{2}} + x^{2}} x