derivative arctan(x/5)

解

導関数

arctan (\frac{x}{5})

\frac{5}{x ^{2} + 25}

解答ステップ

\frac{d}{d x} (arctan (\frac{x}{5}))

連鎖法則を適用:

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

= \frac{1}{( \frac{x}{5} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= \frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5}

簡素化

\frac{1}{( \frac{x}{5} ) ^{2} + 1} \cdot \frac{1}{5} : \frac{5}{x ^{2} + 25}

= \frac{5}{x ^{2} + 25}