derivative arctan(4x)

解

導関数

arctan (4 x)

\frac{4}{16 x ^{2} + 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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