derivative of (arctan(2x)^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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}

簡素化

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}