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Beliebt Rechnen >

derivative (arctan(x))^2

Lösung

ableitung von

(arctan (x))^{2}

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= 2 arctan (x) \frac{d}{d x} (arctan (x))

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

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

Vereinfache

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

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

Graph

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