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Beliebt Rechnen >

derivative of (1+x^{-1}^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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