derivative arctan(16x)

解

導関数

arctan (16 x)

\frac{16}{256 x ^{2} + 1}

解答ステップ

\frac{d}{d x} (arctan (16 x))

連鎖法則を適用:

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

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

\frac{d}{d x} (16 x) = 16

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

簡素化

\frac{1}{( 16 x ) ^{2} + 1} \cdot 16 : \frac{16}{256 x ^{2} + 1}

= \frac{16}{256 x ^{2} + 1}