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Beliebt Rechnen >

derivative ln(1+1/x)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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