(\partial)/(\partial x)((z)(x^2e^y-yze^x))

Lösung

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} - yz e^{x}))

z (2 e^{y} x - yz e^{x})

Schritte zur Lösung

\frac{\partial}{\partial x} ((z) (x^{2} e^{y} - yz e^{x}))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{2} e^{y}) = 2 e^{y} x

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

= z (2 e^{y} x - yz e^{x})

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