What is the derivative of f(x)=tan(1/x) ?

The derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)

What is the first derivative of f(x)=tan(1/x) ?

The first derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)

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derivative of

f (x) = tan (\frac{1}{x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of f(x)=tan(1/x) ?
The derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)
What is the first derivative of f(x)=tan(1/x) ?
The first derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)