簡約 d/(d^2x)(e^{-x^2})

解

簡約

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

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

解答ステップ

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

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{d}{d ^{2} x} \cdot \frac{1}{e ^{x^{2}}}

\frac{d}{d ^{2} x} = \frac{1}{d x}

= \frac{1}{d x} \cdot \frac{1}{e ^{x^{2}}}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{d x e ^{x^{2}}}

数を乗じる:

1 \cdot 1 = 1

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