derivative of e^{4x^2}*8x

Lösung

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

8 (8 e^{4 x^{2}} x^{2} + e^{4 x^{2}})

Schritte zur Lösung

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

Entferne die Konstante:

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

= 8 \frac{d}{d x} (e^{4 x^{2}} x)

Wende die Produktregel an:

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

f = e^{4 x^{2}}, g = x

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

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

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

= 8 (e^{4 x^{2}} \cdot 8 xx + 1 \cdot e^{4 x^{2}})

Vereinfache

8 (e^{4 x^{2}} \cdot 8 xx + 1 \cdot e^{4 x^{2}}) : 8 (8 e^{4 x^{2}} x^{2} + e^{4 x^{2}})

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

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