derivative y=(arctan(3x))^2

解

導関数

y = (arctan (3 x))^{2}

\frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

解答ステップ

\frac{d}{d x} ((arctan (3 x))^{2})

連鎖法則を適用:

2 arctan (3 x) \frac{d}{d x} (arctan (3 x))

= 2 arctan (3 x) \frac{d}{d x} (arctan (3 x))

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= 2 arctan (3 x) \frac{3}{9 x ^{2} + 1}

簡素化

2 arctan (3 x) \frac{3}{9 x ^{2} + 1} : \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

= \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}