derivative of (x-1/x ^3)

Lösung

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

3 x^{2} + \frac{3}{x ^{4}} - \frac{3}{x ^{2}} - 3

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= 3 x^{2} + \frac{3}{x ^{4}} - \frac{3}{x ^{2}} - 3

\int \frac{7 x ^{3} + 7 x}{x - 1} d x

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