derivative arcsin(2/(x^2))

解

derivative

- \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}

解答ステップ

\frac{d}{d x} (arcsin (\frac{2}{x ^{2}}))

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{2}{x ^{2}}) = - \frac{4}{x ^{3}}

= \frac{1}{1 - ( \frac{2}{x ^{2}} ) ^{2}} (- \frac{4}{x ^{3}})

簡素化

\frac{1}{1 - ( \frac{2}{x ^{2}} ) ^{2}} (- \frac{4}{x ^{3}}) : - \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}

= - \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}