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Beliebt Rechnen >

derivative f(x)= 2/(x-1)

Lösung

ableitung von

f (x) = \frac{2}{x - 1}

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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