derivative of ln(arctan(9x^4))

解

\frac{d}{d x} (ln (arctan (9 x^{4})))

\frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}

解答ステップ

\frac{d}{d x} (ln (arctan (9 x^{4})))

連鎖法則を適用:

\frac{1}{arctan ( 9 x ^{4} )} \frac{d}{d x} (arctan (9 x^{4}))

= \frac{1}{arctan ( 9 x ^{4} )} \frac{d}{d x} (arctan (9 x^{4}))

\frac{d}{d x} (arctan (9 x^{4})) = \frac{36 x ^{3}}{81 x ^{8} + 1}

= \frac{1}{arctan ( 9 x ^{4} )} \cdot \frac{36 x ^{3}}{81 x ^{8} + 1}

簡素化

\frac{1}{arctan ( 9 x ^{4} )} \cdot \frac{36 x ^{3}}{81 x ^{8} + 1} : \frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}

= \frac{36 x ^{3}}{arctan ( 9 x ^{4} ) ( 81 x ^{8} + 1 )}