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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Graph

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