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Beliebt Rechnen >

(e^t(5-3e^{-2t}))^'

Lösung

(e^{t} (5 - 3 e^{- 2 t}))^{^{'}}

Lösung

5 e^{t} + 3 e^{- t}

Schritte zur Lösung

(e^{t} (5 - 3 e^{- 2 t}))^{'}

Wende die Produktregel an:

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

f = e^{t}, g = 5 - 3 e^{- 2 t}

= (e^{t})^{^{'}} (5 - 3 e^{- 2 t}) + (5 - 3 e^{- 2 t})^{^{'}} e^{t}

(e^{t})^{'} = e^{t}

(5 - 3 e^{- 2 t})^{'} = 6 e^{- 2 t}

= e^{t} (5 - 3 e^{- 2 t}) + 6 e^{- 2 t} e^{t}

Vereinfache

e^{t} (5 - 3 e^{- 2 t}) + 6 e^{- 2 t} e^{t} : 5 e^{t} + 3 e^{- t}

= 5 e^{t} + 3 e^{- t}

Graph

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