(\partial)/(\partial z)(6x^{y/z})

Lösung

\frac{\partial}{\partial z} (6 x^{\frac{y}{z}})

- \frac{6 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial z} (6 x^{\frac{y}{z}})

Behandle

x, y

als Konstanten

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial z} (x^{\frac{y}{z}})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

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

= 6 \frac{\partial}{\partial z} (e^{\frac{y}{z} l n (x)})

Wende die Kettenregel an:

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

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

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

= 6 e^{\frac{y}{z} l n (x)} (- \frac{y ln ( x )}{z ^{2}})

Vereinfache

6 e^{\frac{y}{z} l n (x)} (- \frac{y ln ( x )}{z ^{2}}) : - \frac{6 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

= - \frac{6 y x ^{\frac{y}{z}} ln ( x )}{z ^{2}}

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