derivative of arctan(x/8)

解

\frac{d}{d x} (arctan (\frac{x}{8}))

\frac{8}{x ^{2} + 64}

解答ステップ

\frac{d}{d x} (arctan (\frac{x}{8}))

連鎖法則を適用:

\frac{1}{( \frac{x}{8} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{8})

= \frac{1}{( \frac{x}{8} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= \frac{1}{( \frac{x}{8} ) ^{2} + 1} \cdot \frac{1}{8}

簡素化

\frac{1}{( \frac{x}{8} ) ^{2} + 1} \cdot \frac{1}{8} : \frac{8}{x ^{2} + 64}

= \frac{8}{x ^{2} + 64}