What is the derivative of arcsec(1/x) ?

The derivative of arcsec(1/x) is -1/(sqrt(1-x^2))

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

The first derivative of arcsec(1/x) is -1/(sqrt(1-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- \frac{1}{1 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{1}{1 - x ^{2}}

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