derivative of 9x^2e^x

Lösung

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

9 (2 x e^{x} + e^{x} x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x^{2}, g = e^{x}

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

\frac{d}{d x} (x^{2}) = 2 x

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

= 9 (2 x e^{x} + e^{x} x^{2})

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