derivative of ln(arctan(8x^5))

解

\frac{d}{d x} (ln (arctan (8 x^{5})))

\frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

解答ステップ

\frac{d}{d x} (ln (arctan (8 x^{5})))

連鎖法則を適用:

\frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

= \frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

\frac{d}{d x} (arctan (8 x^{5})) = \frac{40 x ^{4}}{64 x ^{10} + 1}

= \frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1}

簡素化

\frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1} : \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

= \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}