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Beliebt Rechnen >

derivative of 1/(x-1+1/(x+1))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

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

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

Graph

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