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Beliebt Rechnen >

derivative f(x)=(x^2+1)(2-x)

Lösung

ableitung von

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

Lösung

4 x - 3 x^{2} - 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (2 - x) + (- 1) (x^{2} + 1) : 4 x - 3 x^{2} - 1

= 4 x - 3 x^{2} - 1

Graph

Beliebte Beispiele

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