tan-1 2x/1-x2
d/dx (( tan^-1)) = 1/( 1 + x^2)
1
d( tan^-1((2x/ 1 - x^2)) = --------------------------d( 2x/(1 - x^2) =
1 + ( 2x/( 1 - x^2))^2
d(2x)*(1 - x^2) - 2xd(1 - x^2) 2(1 - x^2) - 2x( - 2x)
d( 2x/(1 - x^2) = --------------------------------------- = ------------------------------ =
( 1 - x^2)^2 ( 1 - x^2)^2
(2 - 2x^2 + 4x^2)/(1 - x^2)^2 =(2+2x^2)/( 1 - x^2)^2 =2(1 +x^2)/(1 - x^2)^2
2(1 +x^2)/(1 - x^2)^2 2(1 +x^2)/(1 - x^2)^2
d = ----------------------------------------- = ------------------------------------------ =
1 + ( 2x/( 1 - x^2))^2 [(1 -x^2)^2 + 2x)]/(1 - x^2)^2
2(1 +x^2)
d = ---------------------------------------
[(1 -x^2)^2 + 2x)]