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Beliebt Rechnen >

derivative of 540(1-e^{-0.1x})

Lösung

\frac{d}{d x} (540 (1 - e^{- 0.1 x}))

Lösung

54 e^{- 0.1 x}

Schritte zur Lösung

\frac{d}{d x} (540 (1 - e^{- 0.1 x}))

Entferne die Konstante:

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

= 540 \frac{d}{d x} (1 - e^{- 0.1 x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 540 (\frac{d}{d x} (1) - \frac{d}{d x} (e^{- 0.1 x}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (e^{- 0.1 x}) = - 0.1 e^{- 0.1 x}

= 540 (0 - (- 0.1 e^{- 0.1 x}))

Vereinfache

= 54 e^{- 0.1 x}

Graph

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