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Beliebt Rechnen >

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

Lösung

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

Lösung

36 x^{3} - 42 x^{6} + 24 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

12 x^{3} (3 - 2 x^{3}) + (- 6 x^{2}) (3 x^{4} - 4) : 36 x^{3} - 42 x^{6} + 24 x^{2}

= 36 x^{3} - 42 x^{6} + 24 x^{2}

Graph

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