derivative of e^x(2x^2+x-8)

Lösung

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

2 e^{x} x^{2} + 5 e^{x} x - 7 e^{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (2 x^{2} + x - 8) = 4 x + 1

= e^{x} (2 x^{2} + x - 8) + (4 x + 1) e^{x}

Vereinfache

e^{x} (2 x^{2} + x - 8) + (4 x + 1) e^{x} : 2 e^{x} x^{2} + 5 e^{x} x - 7 e^{x}

= 2 e^{x} x^{2} + 5 e^{x} x - 7 e^{x}

\int - 4 x^{4} + 8 x^{3} d x

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