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Beliebt Rechnen >

derivative of e^{sqrt(2x)}(sqrt(2x)-1)

Lösung

\frac{d}{d x} (e^{2 x} (2 x - 1))

Lösung

e^{2 x}

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} (2 x - 1))

Vereinfache

e^{2 x} (2 x - 1) : e^{2 x} (2 x - 1)

= \frac{d}{d x} (e^{2 x} (2 x - 1))

Wende die Produktregel an:

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

f = e^{2 x}, g = 2 x - 1

= \frac{d}{d x} (e^{2 x}) (2 x - 1) + \frac{d}{d x} (2 x - 1) e^{2 x}

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

\frac{d}{d x} (2 x - 1) = \frac{1}{2 x}

= \frac{e ^{2 x}}{2 x} (2 x - 1) + \frac{1}{2 x} e^{2 x}

Vereinfache

\frac{e ^{2 x}}{2 x} (2 x - 1) + \frac{1}{2 x} e^{2 x} : e^{2 x}

= e^{2 x}

Graph

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