derivative (arctan(8x))^2

解

導関数

(arctan (8 x))^{2}

\frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

解答ステップ

\frac{d}{d x} ((arctan (8 x))^{2})

連鎖法則を適用:

2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

= 2 arctan (8 x) \frac{d}{d x} (arctan (8 x))

\frac{d}{d x} (arctan (8 x)) = \frac{8}{64 x ^{2} + 1}

= 2 arctan (8 x) \frac{8}{64 x ^{2} + 1}

簡素化

2 arctan (8 x) \frac{8}{64 x ^{2} + 1} : \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}

= \frac{16 arctan ( 8 x )}{64 x ^{2} + 1}