derivative arctan(x/3)

解

導関数

arctan (\frac{x}{3})

\frac{3}{x ^{2} + 9}

解答ステップ

\frac{d}{d x} (arctan (\frac{x}{3}))

連鎖法則を適用:

\frac{1}{( \frac{x}{3} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{3})

= \frac{1}{( \frac{x}{3} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{3})

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= \frac{1}{( \frac{x}{3} ) ^{2} + 1} \cdot \frac{1}{3}

簡素化

\frac{1}{( \frac{x}{3} ) ^{2} + 1} \cdot \frac{1}{3} : \frac{3}{x ^{2} + 9}

= \frac{3}{x ^{2} + 9}