derivative of (7x^2-12xe^x)

Lösung

\frac{d}{d x} ((7 x^{2} - 12 x) e^{x})

7 e^{x} x^{2} + 2 e^{x} x - 12 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((7 x^{2} - 12 x) e^{x})

Wende die Produktregel an:

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

f = 7 x^{2} - 12 x, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 12 x) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 12 x)

\frac{d}{d x} (7 x^{2} - 12 x) = 14 x - 12

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

= (14 x - 12) e^{x} + e^{x} (7 x^{2} - 12 x)

Vereinfache

(14 x - 12) e^{x} + e^{x} (7 x^{2} - 12 x) : 7 e^{x} x^{2} + 2 e^{x} x - 12 e^{x}

= 7 e^{x} x^{2} + 2 e^{x} x - 12 e^{x}

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