derivative 1/(cot(1/t))

解

導関数

\frac{1}{cot ( \frac{1}{t} )}

- \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}

解答ステップ

\frac{d}{d t} (\frac{1}{cot ( \frac{1}{t} )})

簡素化

\frac{1}{cot ( \frac{1}{t} )} : tan (\frac{1}{t})

= \frac{d}{d t} (tan (\frac{1}{t}))

連鎖法則を適用:

sec^{2} (\frac{1}{t}) \frac{d}{d t} (\frac{1}{t})

= sec^{2} (\frac{1}{t}) \frac{d}{d t} (\frac{1}{t})

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

= sec^{2} (\frac{1}{t}) (- \frac{1}{t ^{2}})

簡素化

sec^{2} (\frac{1}{t}) (- \frac{1}{t ^{2}}) : - \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}

= - \frac{sec ^{2} ( \frac{1}{t} )}{t ^{2}}