derivative 12(x-1/x)^4

Lösung

ableitung von

12 (x - \frac{1}{x})^{4}

48 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

Schritte zur Lösung

\frac{d}{d x} (12 (x - \frac{1}{x})^{4})

Entferne die Konstante:

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

= 12 \frac{d}{d x} ((x - \frac{1}{x})^{4})

Wende die Kettenregel an:

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

= 4 (x - \frac{1}{x})^{3} \frac{d}{d x} (x - \frac{1}{x})

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

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

Vereinfache

= 48 (x - \frac{1}{x})^{3} (1 + \frac{1}{x ^{2}})

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