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Beliebt Rechnen >

(arctan(1/x))^'

Lösung

(arctan (\frac{1}{x}))^{^{'}}

Lösung

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

Schritte zur Lösung

(arctan (\frac{1}{x}))^{'}

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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