Question 1178008
 find the derivative of {{{y=arcsec( x) }}}by using {{{1/x=cos(y)}}}


{{{y=arcsec(x)=1/arccos (x)=arccos (1/x)}}}

let {{{1/x=u}}}


{{{(d/dx)(arccos(u))=1/(sqrt(1-(1/x))^2)}}}*{{{u}}}’


{{{(dy/dx)=(-1/(sqrt(1-(1/x))^2))*(-1/x^2)}}}

{{{(dy/dx)=1/(x^2*sqrt(1-(1/x))^2)}}}


you obtain {{{ dy/dx= 1/(x^2 *sqrt(x^2-1)) }}}, and this part {{{sqrt(x^2-1)}}} is incorrect , suppose to be {{{sqrt(1-x^2)}}}