derivative of e^{x/(x-1})

Lösung

\frac{d}{d x} (e^{\frac{x}{x - 1}})

- \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{\frac{x}{x - 1}})

Wende die Kettenregel an:

e^{\frac{x}{x - 1}} \frac{d}{d x} (\frac{x}{x - 1})

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

\frac{d}{d x} (\frac{x}{x - 1}) = - \frac{1}{( x - 1 ) ^{2}}

= e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}})

Vereinfache

e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}}) : - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

= - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

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