derivative of arctan^2(x^3)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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