derivative of e^xx^3

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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