derivative e^{1-x}*(5-x^2)

Lösung

ableitung von

e^{1 - x} \cdot (5 - x^{2})

- e^{1 - x} (5 - x^{2}) - 2 e^{1 - x} x

Schritte zur Lösung

\frac{d}{d x} (e^{1 - x} (5 - x^{2}))

Wende die Produktregel an:

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

f = e^{1 - x}, g = 5 - x^{2}

= \frac{d}{d x} (e^{1 - x}) (5 - x^{2}) + \frac{d}{d x} (5 - x^{2}) e^{1 - x}

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

\frac{d}{d x} (5 - x^{2}) = - 2 x

= (- e^{1 - x}) (5 - x^{2}) + (- 2 x) e^{1 - x}

Vereinfache

= - e^{1 - x} (5 - x^{2}) - 2 e^{1 - x} x

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