(\partial}{\partial x}(e^{\frac{xy)/z})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (\frac{x y}{z}) = \frac{y}{z}

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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