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Beliebt Rechnen >

derivative of (x^3-6x(2-4x^3))

Lösung

\frac{d}{d x} ((x^{3} - 6 x) (2 - 4 x^{3}))

Lösung

- 24 x^{5} + 96 x^{3} + 6 x^{2} - 12

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 6 x) (2 - 4 x^{3}))

Wende die Produktregel an:

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

f = x^{3} - 6 x, g = 2 - 4 x^{3}

= \frac{d}{d x} (x^{3} - 6 x) (2 - 4 x^{3}) + \frac{d}{d x} (2 - 4 x^{3}) (x^{3} - 6 x)

\frac{d}{d x} (x^{3} - 6 x) = 3 x^{2} - 6

\frac{d}{d x} (2 - 4 x^{3}) = - 12 x^{2}

= (3 x^{2} - 6) (2 - 4 x^{3}) + (- 12 x^{2}) (x^{3} - 6 x)

Vereinfache

(3 x^{2} - 6) (2 - 4 x^{3}) + (- 12 x^{2}) (x^{3} - 6 x) : - 24 x^{5} + 96 x^{3} + 6 x^{2} - 12

= - 24 x^{5} + 96 x^{3} + 6 x^{2} - 12

Graph

Beliebte Beispiele

integral of x(b-x)^2

\int x (b - x)^{2} d x

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\int \frac{y}{3 + y ^{2}} d y

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\int \frac{1}{w} d w

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