derivative y=arccos((11)/x)

解

導関数

y = arccos (\frac{11}{x})

\frac{11 x ^{2}}{x ^{2} x ^{2} - 121}

解答ステップ

\frac{d}{d x} (arccos (\frac{11}{x}))

連鎖法則を適用:

- \frac{1}{1 - ( \frac{11}{x} ) ^{2}} \frac{d}{d x} (\frac{11}{x})

= - \frac{1}{1 - ( \frac{11}{x} ) ^{2}} \frac{d}{d x} (\frac{11}{x})

\frac{d}{d x} (\frac{11}{x}) = - \frac{11}{x ^{2}}

= - \frac{1}{1 - ( \frac{11}{x} ) ^{2}} (- \frac{11}{x ^{2}})

簡素化

- \frac{1}{1 - ( \frac{11}{x} ) ^{2}} (- \frac{11}{x ^{2}}) : \frac{11 x ^{2}}{x ^{2} x ^{2} - 121}

= \frac{11 x ^{2}}{x ^{2} x ^{2} - 121}