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Beliebt Rechnen >

derivative of x(1-x^6)

Lösung

\frac{d}{d x} (x (1 - x)^{6})

Lösung

(1 - x)^{6} - 6 x (1 - x)^{5}

Schritte zur Lösung

\frac{d}{d x} (x (1 - x)^{6})

Wende die Produktregel an:

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

f = x, g = (1 - x)^{6}

= \frac{d x}{d x} (1 - x)^{6} + \frac{d}{d x} ((1 - x)^{6}) x

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

\frac{d}{d x} ((1 - x)^{6}) = - 6 (1 - x)^{5}

= 1 \cdot (1 - x)^{6} + (- 6 (1 - x)^{5}) x

Vereinfache

= (1 - x)^{6} - 6 x (1 - x)^{5}

Graph

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