" 5."tan^(-1)(sqrt(1+x^(2))-1)/(x)*x+0

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

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

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

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

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 .