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Beliebt Rechnen >

derivative f(x)=ln((x+1)/(x-1))

Lösung

ableitung von

f (x) = ln (\frac{x + 1}{x - 1})

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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