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Beliebt Rechnen >

derivative y=e^x(3-5x+3x^2)

Lösung

ableitung von

y = e^{x} (3 - 5 x + 3 x^{2})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (e^{x} (3 - 5 x + 3 x^{2}))

Wende die Produktregel an:

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

f = e^{x}, g = 3 - 5 x + 3 x^{2}

= \frac{d}{d x} (e^{x}) (3 - 5 x + 3 x^{2}) + \frac{d}{d x} (3 - 5 x + 3 x^{2}) e^{x}

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

\frac{d}{d x} (3 - 5 x + 3 x^{2}) = 6 x - 5

= e^{x} (3 - 5 x + 3 x^{2}) + (6 x - 5) e^{x}

Vereinfache

e^{x} (3 - 5 x + 3 x^{2}) + (6 x - 5) e^{x} : 3 e^{x} x^{2} + e^{x} x - 2 e^{x}

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

Graph

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