derivative of e^{x/(x-8})

解

\frac{d}{d x} (e^{\frac{x}{x - 8}})

- \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}

解答ステップ

\frac{d}{d x} (e^{\frac{x}{x - 8}})

連鎖法則を適用:

e^{\frac{x}{x - 8}} \frac{d}{d x} (\frac{x}{x - 8})

= e^{\frac{x}{x - 8}} \frac{d}{d x} (\frac{x}{x - 8})

\frac{d}{d x} (\frac{x}{x - 8}) = - \frac{8}{( x - 8 ) ^{2}}

= e^{\frac{x}{x - 8}} (- \frac{8}{( x - 8 ) ^{2}})

簡素化

e^{\frac{x}{x - 8}} (- \frac{8}{( x - 8 ) ^{2}}) : - \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}

= - \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}