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Popular Calculus >

derivative of tan(2/x)

Solution

\frac{d}{d x} (tan (\frac{2}{x}))

Solution

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

Solution steps

\frac{d}{d x} (tan (\frac{2}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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