derivative cos(2arctan(x))

解

導関数

cos (2 arctan (x))

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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