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

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

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

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

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

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)))

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

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

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

If x sqrt(1+y)+y sqrt(1+x)=0, then prove that (dy)/(dx)=-(1+x)^(-2)

If x sqrt(1+y)+y sqrt(1+x)=0, prove that (dy)/(dx)=-(1)/((x+1)^(2))