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Beliebt Rechnen >

derivative 1/(ln(x+1))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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