(\partial)/(\partial x)(e^{y/x})

Lösung

\frac{\partial}{\partial x} (e^{\frac{y}{x}})

- \frac{e ^{\frac{y}{x}} y}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{\frac{y}{x}})

Behandle

y

als Konstante

Wende die Kettenregel an:

e^{\frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

= e^{\frac{y}{x}} \frac{\partial}{\partial x} (\frac{y}{x})

\frac{\partial}{\partial x} (\frac{y}{x}) = - \frac{y}{x ^{2}}

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

Vereinfache

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

= - \frac{e ^{\frac{y}{x}} y}{x ^{2}}

\int x^{2} + 3 d x

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\frac{\partial}{\partial x} (5 - x^{2} + x y - 3 y^{2})