What is the derivative of 1/(cot(1/t)) ?

The derivative of 1/(cot(1/t)) is -(sec^2(1/t))/(t^2)

What is the first derivative of 1/(cot(1/t)) ?

The first derivative of 1/(cot(1/t)) is -(sec^2(1/t))/(t^2)

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derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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}})

Simplify

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}}

What is the derivative of 1/(cot(1/t)) ?
The derivative of 1/(cot(1/t)) is -(sec^2(1/t))/(t^2)
What is the first derivative of 1/(cot(1/t)) ?
The first derivative of 1/(cot(1/t)) is -(sec^2(1/t))/(t^2)