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Beliebt Rechnen >

derivative of 8(x^3-x^4)

Lösung

\frac{d}{d x} (8 (x^{3} - x)^{4})

Lösung

32 (x^{3} - x)^{3} (3 x^{2} - 1)

Schritte zur Lösung

\frac{d}{d x} (8 (x^{3} - x)^{4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} ((x^{3} - x)^{4})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{3} - x) = 3 x^{2} - 1

= 8 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Vereinfache

= 32 (x^{3} - x)^{3} (3 x^{2} - 1)

Graph

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