derivative (3x^2+5)e^{4x}

Lösung

ableitung von

(3 x^{2} + 5) e^{4 x}

6 x e^{4 x} + e^{4 x} \cdot 4 (3 x^{2} + 5)

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} + 5) e^{4 x})

Wende die Produktregel an:

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

f = 3 x^{2} + 5, g = e^{4 x}

= \frac{d}{d x} (3 x^{2} + 5) e^{4 x} + \frac{d}{d x} (e^{4 x}) (3 x^{2} + 5)

\frac{d}{d x} (3 x^{2} + 5) = 6 x

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

= 6 x e^{4 x} + e^{4 x} \cdot 4 (3 x^{2} + 5)

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