derivative 9(x^3-x)^4

Lösung

ableitung von

9 (x^{3} - x)^{4}

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

Schritte zur Lösung

\frac{d}{d x} (9 (x^{3} - x)^{4})

Entferne die Konstante:

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

= 9 \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

= 9 \cdot 4 (x^{3} - x)^{3} (3 x^{2} - 1)

Vereinfache

= 36 (x^{3} - x)^{3} (3 x^{2} - 1)

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