derivative of arctan(x^3-1)

解

\frac{d}{d x} (arctan (x^{3} - 1))

\frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}

解答ステップ

\frac{d}{d x} (arctan (x^{3} - 1))

連鎖法則を適用:

\frac{1}{( x ^{3} - 1 ) ^{2} + 1} \frac{d}{d x} (x^{3} - 1)

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

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

= \frac{1}{( x ^{3} - 1 ) ^{2} + 1} \cdot 3 x^{2}

簡素化

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

= \frac{3 x ^{2}}{x ^{6} - 2 x ^{3} + 2}