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Beliebt Rechnen >

derivative of x^3(4x^2-5x-6)

Lösung

\frac{d}{d x} (x^{3} (4 x^{2} - 5 x - 6))

Lösung

20 x^{4} - 20 x^{3} - 18 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (4 x^{2} - 5 x - 6))

Wende die Produktregel an:

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

f = x^{3}, g = 4 x^{2} - 5 x - 6

= \frac{d}{d x} (x^{3}) (4 x^{2} - 5 x - 6) + \frac{d}{d x} (4 x^{2} - 5 x - 6) x^{3}

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

\frac{d}{d x} (4 x^{2} - 5 x - 6) = 8 x - 5

= 3 x^{2} (4 x^{2} - 5 x - 6) + (8 x - 5) x^{3}

Vereinfache

3 x^{2} (4 x^{2} - 5 x - 6) + (8 x - 5) x^{3} : 20 x^{4} - 20 x^{3} - 18 x^{2}

= 20 x^{4} - 20 x^{3} - 18 x^{2}

Graph

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