derivative of arctan(1/(x^2))

Lösung

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

- \frac{2 x}{1 + x ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= \frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} (- \frac{2}{x ^{3}})

Vereinfache

\frac{1}{( \frac{1}{x ^{2}} ) ^{2} + 1} (- \frac{2}{x ^{3}}) : - \frac{2 x}{1 + x ^{4}}

= - \frac{2 x}{1 + x ^{4}}

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