11.tan^(-1)[(sqrt(1+x^(2))-1)/(x)]quad [2003,12]

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

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

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

Prove that tan^(-1)backslash(sqrt(1+x^(2))-1)/(x)=(1)/(2)tan^(-1)x

The derivative of Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1) "" (2x sqrt(1-x ^(2)))/(1 - 2 x ^(2))at x =0 is

Find the derivative of tan^(-1) "" (sqrt(1 + x^(2)) - 1)/( x) with respect to tan^(-1) ( 2 x sqrt( 1 - x^(2)))/(1 - 2 x ^(2)) at x = 0

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