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Popular >

derivative of sec(1/x)

Solution

derivative of

sec (\frac{1}{x})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(ln(x+4y))

\frac{\partial}{\partial x} (ln (x + 4 y))

integral of sin(7x)sin(9x)

\int sin (7 x) sin (9 x) d x

y^'+(1-2x)/(x^2)y=1

y^{^{'}} + \frac{1 - 2 x}{x ^{2}} y = 1

(\partial)/(\partial y)(2xy^4-1)

\frac{\partial}{\partial y} (2 x y^{4} - 1)

derivative of (5x^2+11x)^{4/3}derivative of

(5 x^{2} + 11 x)^{\frac{4}{3}}

Frequently Asked Questions (FAQ)

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