(" simplely ")/(tan^(-1)sqrt((1-x)/(1+x)))

tan^(-1)((sqrt(x))/(1+20x))

tan^(-1)((x)/(sqrt(1-x)))

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

If y = tan^(-1) {(x)/(1 + sqrt(1 - x^(2)))} + sin { 2 tan^(-1) sqrt((1 - x)/(1 + x))}, "then" (dy)/(dx) =

"tan^(-1)"((sqrt(x)-x)/(1+sqrt(x^(3))))"

(iv) If y=tan^(-1)(x/(1+sqrt(1-x^(2))))+sin(2tan^(-1)sqrt((1-x)/(1+x))) , then find (dy)/(dx) for x epsilon(-1,1)

sqrt((1-tan x)/(1+tan x))