derivative of (9x^2-16xe^x)

Lösung

\frac{d}{d x} ((9 x^{2} - 16 x) e^{x})

9 e^{x} x^{2} + 2 e^{x} x - 16 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((9 x^{2} - 16 x) e^{x})

Wende die Produktregel an:

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

f = 9 x^{2} - 16 x, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 16 x) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 16 x)

\frac{d}{d x} (9 x^{2} - 16 x) = 18 x - 16

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

= (18 x - 16) e^{x} + e^{x} (9 x^{2} - 16 x)

Vereinfache

(18 x - 16) e^{x} + e^{x} (9 x^{2} - 16 x) : 9 e^{x} x^{2} + 2 e^{x} x - 16 e^{x}

= 9 e^{x} x^{2} + 2 e^{x} x - 16 e^{x}

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