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Beliebt Rechnen >

derivative x(x-1)^2

Lösung

ableitung von

x (x - 1)^{2}

Lösung

3 x^{2} - 4 x + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

Graph

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