`y=sin^(- 1)((2x)/(1+x^2))`,prove that` (1+x^2)(dy)/(dx)=2`

if y=(sin^(-1)x)/(sqrt(1-x^(2))), prove that (1-x^(2))(dy)/(dx)=xy+1

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

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

If y = (sin^-1x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy/dx)- xy = 1

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

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

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , prove that (dy)/(dx) = 4/(1 + x^2) , 0 < x < 1

If y=(sin^(-1)x)/(sqrt(1-x^(2))) , the prove that (1-x^(2))(d^(2)y)/(dx^(2))-3x(dy)/(dx)-y=0 .

If y= sin^(-1)((2x)/(1+x^2)) + sec^(-1)((1+x^2)/(1-x^2)) , prove that (dy)/(dx)=4/(1+x^2) .