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Beliebt Rechnen >

derivative of (1+8x^2(x-x^2))

Lösung

\frac{d}{d x} ((1 + 8 x^{2}) (x - x^{2}))

Lösung

- 32 x^{3} + 24 x^{2} - 2 x + 1

Schritte zur Lösung

\frac{d}{d x} ((1 + 8 x^{2}) (x - x^{2}))

Wende die Produktregel an:

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

f = 1 + 8 x^{2}, g = x - x^{2}

= \frac{d}{d x} (1 + 8 x^{2}) (x - x^{2}) + \frac{d}{d x} (x - x^{2}) (1 + 8 x^{2})

\frac{d}{d x} (1 + 8 x^{2}) = 16 x

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

= 16 x (x - x^{2}) + (1 - 2 x) (1 + 8 x^{2})

Vereinfache

16 x (x - x^{2}) + (1 - 2 x) (1 + 8 x^{2}) : - 32 x^{3} + 24 x^{2} - 2 x + 1

= - 32 x^{3} + 24 x^{2} - 2 x + 1

Graph

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