derivative of 2xe^{x+3}+e^{x+3}x^2

Lösung

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

e^{x + 3} x^{2} + 4 e^{x + 3} x + 2 e^{x + 3}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 (e^{x + 3} + e^{x + 3} x) + e^{x + 3} x^{2} + 2 x e^{x + 3}

Vereinfache

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

= e^{x + 3} x^{2} + 4 e^{x + 3} x + 2 e^{x + 3}

s l o p e e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

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