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Beliebt Rechnen >

derivative 14e^{x^2}x

Lösung

ableitung von

14 e^{x^{2}} x

Lösung

14 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Schritte zur Lösung

\frac{d}{d x} (14 e^{x^{2}} x)

Entferne die Konstante:

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

= 14 \frac{d}{d x} (e^{x^{2}} x)

Wende die Produktregel an:

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

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

= 14 (\frac{d}{d x} (e^{x^{2}}) x + \frac{d x}{d x} e^{x^{2}})

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

\frac{d x}{d x} = 1

= 14 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}})

Vereinfache

14 (e^{x^{2}} \cdot 2 xx + 1 \cdot e^{x^{2}}) : 14 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 14 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Graph

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