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Beliebt Rechnen >

derivative y=(arctan(4x))^2

Lösung

ableitung von

y = (arctan (4 x))^{2}

Lösung

\frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

2 arctan (4 x) \frac{d}{d x} (arctan (4 x))

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= 2 arctan (4 x) \frac{4}{16 x ^{2} + 1}

Vereinfache

2 arctan (4 x) \frac{4}{16 x ^{2} + 1} : \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

= \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

Graph

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