derivative of tan(2/x)

Lösung

\frac{d}{d x} (tan (\frac{2}{x}))

- \frac{2 sec ^{2} ( \frac{2}{x} )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (tan (\frac{2}{x}))

Wende die Kettenregel an:

sec^{2} (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

= sec^{2} (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

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

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

Vereinfache

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

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

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