If `y =log sqrt((x^2+x+1)/(x^2-x+1))+1/(2sqrt3){tan^(-1)\ (2x+1)/sqrt3+tan^(-1)\ (2x-1)/sqrt3}` then prove that `dy/dx=1/(x^4+x^2+1)`

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=tan^(-1)(sqrt(1+x^(2))-x) then,prove that (dy)/(dx)=-(1)/(2(x^(2)+1))

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

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)

If y = tan ^ (- 1) ((3x) / (1-2x ^ (2))), - (1) / (sqrt (2))

If 3Tan^(-1)(1/(2+sqrt3))-Tan^(-1)(1/x)=Tan^(-1)(1/3) , then x =

Let y=1/3 log\ (x+1)/sqrt(x^2-x+1)+1/sqrt3 tan^-1\ (2x-1)/sqrt3 statement 1: dy/dx at x=0 is 1 statement 2: (dy)/(dx)=2/(x^3+2)

If y=log(sqrt(x)+(1)/(sqrt(x))), prove that (dy)/(dx)=(x-1)/(2x(x+1))

y = tan^(-1)((3x-x^3)/(1-3x^2)), 1/(sqrt3) , x , 1/(sqrt3) .

If y=tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))] then prove that (dy)/(dx)=(1)/(2sqrt(1-x^(2)))