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Beliebt Rechnen >

derivative C(t)=0.0225te^{-0.0467t}

Lösung

ableitung von

C (t) = 0.0225 t e^{- 0.0467 t}

Lösung

0.0225 (e^{- 0.0467 t} - 0.0467 e^{- 0.0467 t} t)

Schritte zur Lösung

\frac{d}{d t} (0.0225 t e^{- 0.0467 t})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.0225 \frac{d}{d t} (t e^{- 0.0467 t})

Wende die Produktregel an:

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

f = t, g = e^{- 0.0467 t}

= 0.0225 (\frac{d t}{d t} e^{- 0.0467 t} + \frac{d}{d t} (e^{- 0.0467 t}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (e^{- 0.0467 t}) = - 0.0467 e^{- 0.0467 t}

= 0.0225 (1 \cdot e^{- 0.0467 t} + (- 0.0467 e^{- 0.0467 t}) t)

Vereinfache

= 0.0225 (e^{- 0.0467 t} - 0.0467 e^{- 0.0467 t} t)

Graph

Beliebte Beispiele

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\int \frac{1}{2} + \frac{x ^{4}}{4} + \frac{1}{4 x ^{4}} d x

y^{''}+4y^'+4y=12t+16

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