derivative cos(2/x)

解

導関数

cos (\frac{2}{x})

\frac{2 sin ( \frac{2}{x} )}{x ^{2}}

解答ステップ

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

連鎖法則を適用:

- sin (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

= - sin (\frac{2}{x}) \frac{d}{d x} (\frac{2}{x})

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

= - sin (\frac{2}{x}) (- \frac{2}{x ^{2}})

簡素化

- sin (\frac{2}{x}) (- \frac{2}{x ^{2}}) : \frac{2 sin ( \frac{2}{x} )}{x ^{2}}

= \frac{2 sin ( \frac{2}{x} )}{x ^{2}}