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

Lösung

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

e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}} x}{y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{\frac{x}{y}}

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}}}{y} x

Vereinfache

1 \cdot e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}}}{y} x : e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}} x}{y}

= e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}} x}{y}

s l o p e (6, - 12), (10, - 8)

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