" What tan "(-sqrt(1+x^(2))-1)/(x),x!=0

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

Write each of the following in the simplest form: tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

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

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 , when x ne 0 .

Differentiate tan^(-1)'(sqrt(1+x^(2))-1)/(x) w.r.t. tan^(-1)x , when x ne 0 .

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t tan^(-1)x , where x ne 0

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

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)