derivative f(x)=6x^2e^{6x}+2xe^{6x}

Lösung

ableitung von

f (x) = 6 x^{2} e^{6 x} + 2 x e^{6 x}

36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} e^{6 x} + 2 x e^{6 x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (6 x^{2} e^{6 x}) + \frac{d}{d x} (2 x e^{6 x})

\frac{d}{d x} (6 x^{2} e^{6 x}) = 6 (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2})

\frac{d}{d x} (2 x e^{6 x}) = 2 (e^{6 x} + 6 e^{6 x} x)

= 6 (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}) + 2 (e^{6 x} + 6 e^{6 x} x)

Vereinfache

6 (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2}) + 2 (e^{6 x} + 6 e^{6 x} x) : 36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

= 36 e^{6 x} x^{2} + 24 e^{6 x} x + 2 e^{6 x}

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