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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} + 1, g = e^{x - 1}

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

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

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

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

Graph

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