Differentiate the functions with respect to `x :` `tan^(-1){(sqrt(1+a^2x^2)-1)/(a x)},x!=0`

Explanation

y=`tan^(-1){(sqrt(1+a^2x^2)-1)/(a x)}`

let`ax=tantheta`

y=`tan^(-1){(sqrt(1+a^2x^2)-1)/(tantheta)}`

=`tan^(-1){(sqrt(1+tan^2theta)-1)/(tantheta)}`

=`tan^(-1){(sectheta-1)/(tantheta)/(tantheta)}`

=`tan^(-1){tan(theta/2)}`

=`theta/2`

y=`1/2tan^(-1)ax`