derivative (x^3-1)^{100}

Lösung

ableitung von

(x^{3} - 1)^{100}

300 x^{2} (x^{3} - 1)^{99}

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 1)^{100})

Wende die Kettenregel an:

100 (x^{3} - 1)^{99} \frac{d}{d x} (x^{3} - 1)

= 100 (x^{3} - 1)^{99} \frac{d}{d x} (x^{3} - 1)

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

= 100 (x^{3} - 1)^{99} \cdot 3 x^{2}

Vereinfache

= 300 x^{2} (x^{3} - 1)^{99}

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