derivative y=ln(arctan(4x))

解

導関数

y = ln (arctan (4 x))

\frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= \frac{1}{arctan ( 4 x )} \cdot \frac{4}{16 x ^{2} + 1}

簡素化

\frac{1}{arctan ( 4 x )} \cdot \frac{4}{16 x ^{2} + 1} : \frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}

= \frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}