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Popular Calculus >

Find the Derivative - d/dx tan(1/x)

Solution

derivative of

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

Solution

- \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}}

Graph

Popular Examples

Find the Antiderivative (cos(2x))/2 integral

\frac{( cos ( 2 x ) )}{2}

Find the Slope and y-intercept (-4,4) , (4,4)slope intercept

(- 4, 4), (4, 4)

Find the Derivative - d/dx x/5 derivative of

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

Find the 2nd Derivative e^(3x)second derivative

e^{3 x}

Find the Derivative - d/dx y=sin(1/x)

\frac{d}{d x} y = sin (\frac{1}{x})

Frequently Asked Questions (FAQ)

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