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Beliebt Rechnen >

(\partial)/(\partial x)(x^3e^x)

Lösung

\frac{\partial}{\partial x} (x^{3} e^{x})

Lösung

3 x^{2} e^{x} + e^{x} x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} e^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = e^{x}

= \frac{\partial}{\partial x} (x^{3}) e^{x} + \frac{\partial}{\partial x} (e^{x}) x^{3}

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} x^{3}

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