derivative (x^3+1)e^x

Lösung

ableitung von

(x^{3} + 1) e^{x}

3 x^{2} e^{x} + e^{x} (x^{3} + 1)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 1) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 1, g = e^{x}

= \frac{d}{d x} (x^{3} + 1) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

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