derivative y=sin(1/x)

解

導関数

y = sin (\frac{1}{x})

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

解答ステップ

\frac{d}{d x} (sin (\frac{1}{x}))

連鎖法則を適用:

cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= cos (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

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

簡素化

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

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