derivative of cos(pi/x)

解

\frac{d}{d x} (cos (\frac{π}{x}))

\frac{π sin ( \frac{π}{x} )}{x ^{2}}

解答ステップ

\frac{d}{d x} (cos (\frac{π}{x}))

連鎖法則を適用:

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

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

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

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

簡素化

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

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