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Beliebt Rechnen >

derivative of ln(arctan(2x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{arctan ( 2 x )} \frac{d}{d x} (arctan (2 x))

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

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

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

Vereinfache

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

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

Graph

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