derivative of 26(2e^{x^2}x^2+e^{x^2})

Lösung

\frac{d}{d x} (26 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

26 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Schritte zur Lösung

\frac{d}{d x} (26 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

Entferne die Konstante:

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

= 26 \frac{d}{d x} (2 e^{x^{2}} x^{2} + e^{x^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 26 (\frac{d}{d x} (2 e^{x^{2}} x^{2}) + \frac{d}{d x} (e^{x^{2}}))

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

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

= 26 (2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x)

Multipliziere aus

2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 26 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

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