derivative y=arcsin(1/x)

Lösung

ableitung von

y = arcsin (\frac{1}{x})

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

Schritte zur Lösung

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

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

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