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Beliebt Rechnen >

derivative e^t(cos(t))

Lösung

ableitung von

e^{t} (cos (t))

Lösung

e^{t} cos (t) - e^{t} sin (t)

Schritte zur Lösung

\frac{d}{d t} (e^{t} cos (t))

Wende die Produktregel an:

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

f = e^{t}, g = cos (t)

= \frac{d}{d t} (e^{t}) cos (t) + \frac{d}{d t} (cos (t)) e^{t}

\frac{d}{d t} (e^{t}) = e^{t}

\frac{d}{d t} (cos (t)) = - sin (t)

= e^{t} cos (t) + (- sin (t)) e^{t}

Vereinfache

= e^{t} cos (t) - e^{t} sin (t)

Graph

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