derivative (arctan(x))^2

解

導関数

(arctan (x))^{2}

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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