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Beliebt Rechnen >

derivative f(x)=e^{-x+1}x-2e^{-x+1}

Lösung

ableitung von

f (x) = e^{- x + 1} x - 2 e^{- x + 1}

Lösung

- e^{- x + 1} x + 3 e^{- x + 1}

Schritte zur Lösung

\frac{d}{d x} (e^{- x + 1} x - 2 e^{- x + 1})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (e^{- x + 1} x) - \frac{d}{d x} (2 e^{- x + 1})

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

\frac{d}{d x} (2 e^{- x + 1}) = - 2 e^{- x + 1}

= - e^{- x + 1} x + e^{- x + 1} - (- 2 e^{- x + 1})

Vereinfache

= - e^{- x + 1} x + 3 e^{- x + 1}

Graph

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