derivative of (arctan(5x)^2)

解

\frac{d}{d x} ((arctan (5 x))^{2})

\frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

解答ステップ

\frac{d}{d x} ((arctan (5 x))^{2})

連鎖法則を適用:

2 arctan (5 x) \frac{d}{d x} (arctan (5 x))

= 2 arctan (5 x) \frac{d}{d x} (arctan (5 x))

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= 2 arctan (5 x) \frac{5}{25 x ^{2} + 1}

簡素化

2 arctan (5 x) \frac{5}{25 x ^{2} + 1} : \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

= \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}