derivative of (8x^2-13xe^x)

Lösung

\frac{d}{d x} ((8 x^{2} - 13 x) e^{x})

8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((8 x^{2} - 13 x) e^{x})

Wende die Produktregel an:

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

f = 8 x^{2} - 13 x, g = e^{x}

= \frac{d}{d x} (8 x^{2} - 13 x) e^{x} + \frac{d}{d x} (e^{x}) (8 x^{2} - 13 x)

\frac{d}{d x} (8 x^{2} - 13 x) = 16 x - 13

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

= (16 x - 13) e^{x} + e^{x} (8 x^{2} - 13 x)

Vereinfache

(16 x - 13) e^{x} + e^{x} (8 x^{2} - 13 x) : 8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

= 8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

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