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Beliebt Rechnen >

derivative of xe^{x^4}

Lösung

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

Lösung

e^{x^{4}} + 4 e^{x^{4}} x^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x^{4}}) = e^{x^{4}} \cdot 4 x^{3}

= 1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x

Vereinfache

1 \cdot e^{x^{4}} + e^{x^{4}} \cdot 4 x^{3} x : e^{x^{4}} + 4 e^{x^{4}} x^{4}

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

Graph

Beliebte Beispiele

d/(d{z)}({x}^2{y}{z})

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