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Beliebt Rechnen >

derivative of (1+1/x ^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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