(\partial)/(\partial x)((z)(e^{7z}-xyz))

Lösung

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

- z^{2} y

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (e^{7 z}) = 0

\frac{\partial}{\partial x} (x yz) = zy

= z (0 - zy)

Vereinfache

z (0 - zy) : - z^{2} y

= - z^{2} y

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