derivative of arccot(x/2)

解

\frac{d}{d x} (arccot (\frac{x}{2}))

- \frac{2}{x ^{2} + 4}

解答ステップ

\frac{d}{d x} (arccot (\frac{x}{2}))

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

簡素化

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

= - \frac{2}{x ^{2} + 4}