derivative ln(arctan(2x^3))

解

導関数

ln (arctan (2 x^{3}))

\frac{6 x ^{2}}{arctan ( 2 x ^{3} ) ( 4 x ^{6} + 1 )}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (arctan (2 x^{3})) = \frac{6 x ^{2}}{4 x ^{6} + 1}

= \frac{1}{arctan ( 2 x ^{3} )} \cdot \frac{6 x ^{2}}{4 x ^{6} + 1}

簡素化

\frac{1}{arctan ( 2 x ^{3} )} \cdot \frac{6 x ^{2}}{4 x ^{6} + 1} : \frac{6 x ^{2}}{arctan ( 2 x ^{3} ) ( 4 x ^{6} + 1 )}

= \frac{6 x ^{2}}{arctan ( 2 x ^{3} ) ( 4 x ^{6} + 1 )}