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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

3 x^{2} - 6 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot (x - 2)^{2} + 2 (x - 2) (x + 1) : 3 x^{2} - 6 x

= 3 x^{2} - 6 x

Graph

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