What is the derivative of sec(1/(sqrt(x))) ?

The derivative of sec(1/(sqrt(x))) is -(sec(1/(sqrt(x)))tan(1/(sqrt(x))))/(2x^{3/2)}

What is the first derivative of sec(1/(sqrt(x))) ?

The first derivative of sec(1/(sqrt(x))) is -(sec(1/(sqrt(x)))tan(1/(sqrt(x))))/(2x^{3/2)}

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

- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{2 x ^{\frac{3}{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}{2 x ^{\frac{3}{2}}}

= sec (\frac{1}{x}) tan (\frac{1}{x}) (- \frac{1}{2 x ^{\frac{3}{2}}})

Simplify

sec (\frac{1}{x}) tan (\frac{1}{x}) (- \frac{1}{2 x ^{\frac{3}{2}}}) : - \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{2 x ^{\frac{3}{2}}}

= - \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} )}{2 x ^{\frac{3}{2}}}

What is the derivative of sec(1/(sqrt(x))) ?
The derivative of sec(1/(sqrt(x))) is -(sec(1/(sqrt(x)))tan(1/(sqrt(x))))/(2x^{3/2)}
What is the first derivative of sec(1/(sqrt(x))) ?
The first derivative of sec(1/(sqrt(x))) is -(sec(1/(sqrt(x)))tan(1/(sqrt(x))))/(2x^{3/2)}