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Beliebt Rechnen >

derivative f(x)=(arctan(8x))^2

Lösung

ableitung von

f (x) = (arctan (8 x))^{2}

Lösung

\frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} ((arctan (8 x))^{2})

Wende die Kettenregel an:

2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

= 2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

\frac{d}{d x} (arctan (8 x)) = \frac{8}{64 x ^{2} + 1}

= 2 arctan (8 x) \frac{8}{64 x ^{2} + 1}

Vereinfache

2 arctan (8 x) \frac{8}{64 x ^{2} + 1} : \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

= \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

Graph

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