derivative of 39e^{1/x}

Lösung

\frac{d}{d x} (39 e^{\frac{1}{x}})

- \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (39 e^{\frac{1}{x}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 39 \frac{d}{d x} (e^{\frac{1}{x}})

Wende die Kettenregel an:

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

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

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

= 39 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Vereinfache

39 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

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