(\partial)/(\partial y)(7ze^{xyz})

Lösung

\frac{\partial}{\partial y} (7 z e^{x yz})

7 e^{z x y} z^{2} x

Schritte zur Lösung

\frac{\partial}{\partial y} (7 z e^{x yz})

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= 7 z \frac{\partial}{\partial y} (e^{x yz})

Wende die Kettenregel an:

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

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

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

= 7 z e^{x yz} z x

Vereinfache

7 z e^{x yz} z x : 7 e^{z x y} z^{2} x

= 7 e^{z x y} z^{2} x

s l o p e g (x) = \frac{- 7 e ^{x}}{5 e ^{x} - 8}

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