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Beliebt Rechnen >

derivative of e^{2x}sin(2x)

Lösung

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

Lösung

e^{2 x} \cdot 2 sin (2 x) + cos (2 x) \cdot 2 e^{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = e^{2 x}, g = sin (2 x)

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= e^{2 x} \cdot 2 sin (2 x) + cos (2 x) \cdot 2 e^{2 x}

Graph

Beliebte Beispiele

derivative of ((sqrt(x))/(x+1))

\frac{d}{d x} (\frac{( x )}{x + 1})

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

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\int 8 e^{2 x} d x

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