(d^2)/(dx^2)(e^{3/x})

解

\frac{d ^{2}}{d x ^{2}} (e^{\frac{3}{x}})

- \frac{3 ( - 3 e ^{\frac{3}{x}} - 2 e ^{\frac{3}{x}} x )}{x ^{4}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (e^{\frac{3}{x}})

\frac{d}{d x} (e^{\frac{3}{x}}) = - \frac{3 e ^{\frac{3}{x}}}{x ^{2}}

= \frac{d}{d x} (- \frac{3 e ^{\frac{3}{x}}}{x ^{2}})

\frac{d}{d x} (- \frac{3 e ^{\frac{3}{x}}}{x ^{2}}) = - \frac{3 ( - 3 e ^{\frac{3}{x}} - 2 e ^{\frac{3}{x}} x )}{x ^{4}}

= - \frac{3 ( - 3 e ^{\frac{3}{x}} - 2 e ^{\frac{3}{x}} x )}{x ^{4}}