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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x e^{4 x} + e^{4 x} \cdot 4 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 x e^{4 x} + e^{4 x} \cdot 4 x^{2}

Graph

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