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Beliebt Rechnen >

derivative y=(arctan(2x))^2

Lösung

ableitung von

y = (arctan (2 x))^{2}

Lösung

\frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (arctan (2 x)) = \frac{2}{4 x ^{2} + 1}

= 2 arctan (2 x) \frac{2}{4 x ^{2} + 1}

Vereinfache

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

= \frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

Graph

Beliebte Beispiele

derivative of arctan(sqrt(x^3))

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derivative of arcsin(5x^2)

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derivative of (3x^2/(x^2+1))

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