derivative of arcsec(1/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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