3,quad tan^(-1)(sqrt(1+x^(2))+x)

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3)) w.r.t tan ^(-1)((x)/(sqrt(1-x^(2))))

Differentiate tan^(-1)x/(1+sqrt((1-x^2))) +{2tan^(-1)sqrt(((1-x)/(1+x)))}sinwdotrdottdotxdot

If y=log(x^(2)+x+1)/(x^(2)-x+1)+(2)/(sqrt(3))tan^(-1)((sqrt(3)x)/(1-x^(2))), find (dy)/(dx)

Prove that, (d)/(dx) ["log" (x^(2) + x + 1)/(x^(2) -x + 1) + (2)/(sqrt3) "tan"^(-1) (sqrt3x)/(1-x^(2))]= (4)/(x^(4 ) + x^(2) + 1)

Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , |x|<1/sqrt3 w.r.t tan^(-1)(x/sqrt(1-x^2))

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

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

Prove that: i) tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y) ii) tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x) iii) tan^(-1)(sinx)/(1+cosx)=x/2

Prove that tan^(-1) ((3x-x^(3))/(1-3x^(2)))=tan^(-1)x +"tan"^(-1)(2x)/(1-x^(2)), |x| lt (1)/(sqrt(3)) .