derivative of sin(5/x)

解

\frac{d}{d x} (sin (\frac{5}{x}))

- \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

解答ステップ

\frac{d}{d x} (sin (\frac{5}{x}))

連鎖法則を適用:

cos (\frac{5}{x}) \frac{d}{d x} (\frac{5}{x})

= cos (\frac{5}{x}) \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= cos (\frac{5}{x}) (- \frac{5}{x ^{2}})

簡素化

cos (\frac{5}{x}) (- \frac{5}{x ^{2}}) : - \frac{5 cos ( \frac{5}{x} )}{x ^{2}}

= - \frac{5 cos ( \frac{5}{x} )}{x ^{2}}