(\partial)/(\partial y)(9x^{8y})

Lösung

\frac{\partial}{\partial y} (9 x^{8 y})

72 x^{8 y} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (9 x^{8 y})

Behandle

x

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial y} (x^{8 y})

Wende Exponentenregel an:

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

x^{8 y} = e^{8 y l n (x)}

= 9 \frac{\partial}{\partial y} (e^{8 y l n (x)})

Wende die Kettenregel an:

e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

= e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

\frac{\partial}{\partial y} (8 y ln (x)) = 8 ln (x)

= 9 e^{8 y l n (x)} \cdot 8 ln (x)

Vereinfache

9 e^{8 y l n (x)} \cdot 8 ln (x) : 72 x^{8 y} ln (x)

= 72 x^{8 y} ln (x)

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