Find the derivative of the function
![\[ f(x) = \arccos \frac{1}{x}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-adcdf055b2a91a1837f909811c2cd9cf_l3.png "Rendered by QuickLaTeX.com")
By definition of arcsecant we know
![\[ f(x) = \arccos \frac{1}{x} = \operatorname{arcsec} x. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-ef9b9419ff06878619b7077f62c8eaa1_l3.png "Rendered by QuickLaTeX.com")
We computed the derivative of 
in this exercise (Section 6.22, Exercise #4) so,
![\[ f'(x) = \frac{1}{|x| \sqrt{x^2 - 1}} \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-2850c408b823b2dd670cd8b4c74a831c_l3.png "Rendered by QuickLaTeX.com")
valid for 
.
Find the derivative of the function
By definition of arcsecant we know
We computed the derivative of in this exercise (Section 6.22, Exercise #4) so,
valid for .