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

tan^(-1)(x+sqrt(1+x^(2)))=

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

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

Differentiate tan^(-1)((sqrt(1+x^(2)-1))/(x)) with respect to tan^(-1)x,x!=0

If y=tan^(-1)((sqrt(1+x^(2))-1)/(x)) and z=tan^(-1)((2x)/(1-x^(2))) , then (dy)/(dz) is equal to -

the derivation of tan ^(-1)((sqrt(1+x^(2))-1)/(x)) with respect to tan^(-1)((2x sqrt(1-x^(2)))/(1-2x^(2)))

s=tan^(-1)((sqrt(1+x^(2))-1)/(x)) and T=tan^(-1)x then (ds)/(dT)