`d/(dx)[tan^(- 1)sqrt(1+x^2)-cot^(-1)(-sqrt(1+x^2))]=`

d/(dx) [tan^(-1)(sqrt(x))] =

d/(dx) [tan^(-1)(sqrt(x))] =

(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=

(d)/(dx)[tan^-1((sqrt(1+x^(2))-1)/(x))]=

d//dx[tan^(-1)((sqrt(x^(2)+a^(2))+x)/(sqrt(x^(2)+a^(2))-x))^(1//2)]

(d)/(dx)[tan^(-1)((x-sqrt(a^(2)-x^(2)))/(x+sqrt(a^(2)-x^(2))))]=

d/dx(tan^-1(x/sqrt(a^2-x^2))=

(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=

Differentiate tan^(-1){(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))} with respect to cos^(-1)x^(2)

Differentiate tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))) w.r.t. cos^(-1)x^(2) .