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Beliebt Rechnen >

derivative of x^3(x-4)

Lösung

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

Lösung

4 x^{3} - 12 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (x - 4) = 1

= 3 x^{2} (x - 4) + 1 \cdot x^{3}

Vereinfache

3 x^{2} (x - 4) + 1 \cdot x^{3} : 4 x^{3} - 12 x^{2}

= 4 x^{3} - 12 x^{2}

Graph

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