derivative of 2xe^{5x}

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x, g = e^{5 x}

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

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

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= 2 (1 \cdot e^{5 x} + e^{5 x} \cdot 5 x)

Vereinfache

= 2 (e^{5 x} + 5 e^{5 x} x)

d er i v a t i v e 8 x^{9}

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