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Beliebt Rechnen >

derivative of arccos(1/x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

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