derivative of arccos(4/x)

解

\frac{d}{d x} (arccos (\frac{4}{x}))

\frac{4}{x x ^{2} - 16}

解答ステップ

\frac{d}{d x} (arccos (\frac{4}{x}))

連鎖法則を適用:

- \frac{1}{1 - ( \frac{4}{x} ) ^{2}} \frac{d}{d x} (\frac{4}{x})

= - \frac{1}{1 - ( \frac{4}{x} ) ^{2}} \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

= - \frac{1}{1 - ( \frac{4}{x} ) ^{2}} (- \frac{4}{x ^{2}})

簡素化

- \frac{1}{1 - ( \frac{4}{x} ) ^{2}} (- \frac{4}{x ^{2}}) : \frac{4}{x x ^{2} - 16}

= \frac{4}{x x ^{2} - 16}