derivative e^x(5x^2-10x+10)

Lösung

ableitung von

e^{x} (5 x^{2} - 10 x + 10)

5 e^{x} x^{2}

Schritte zur Lösung

\frac{d}{d x} (e^{x} (5 x^{2} - 10 x + 10))

Wende die Produktregel an:

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

f = e^{x}, g = 5 x^{2} - 10 x + 10

= \frac{d}{d x} (e^{x}) (5 x^{2} - 10 x + 10) + \frac{d}{d x} (5 x^{2} - 10 x + 10) e^{x}

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

\frac{d}{d x} (5 x^{2} - 10 x + 10) = 10 x - 10

= e^{x} (5 x^{2} - 10 x + 10) + (10 x - 10) e^{x}

Vereinfache

e^{x} (5 x^{2} - 10 x + 10) + (10 x - 10) e^{x} : 5 e^{x} x^{2}

= 5 e^{x} x^{2}

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