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Beliebt Rechnen >

derivative e^θsin(5θ)

Lösung

ableitung von

e^{θ} sin (5 θ)

Lösung

e^{θ} sin (5 θ) + cos (5 θ) \cdot 5 e^{θ}

Schritte zur Lösung

\frac{d}{d θ} (e^{θ} sin (5 θ))

Wende die Produktregel an:

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

f = e^{θ}, g = sin (5 θ)

= \frac{d}{d θ} (e^{θ}) sin (5 θ) + \frac{d}{d θ} (sin (5 θ)) e^{θ}

\frac{d}{d θ} (e^{θ}) = e^{θ}

\frac{d}{d θ} (sin (5 θ)) = cos (5 θ) \cdot 5

= e^{θ} sin (5 θ) + cos (5 θ) \cdot 5 e^{θ}

Graph

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