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

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

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

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

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

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

If ysqrt(1-x^2)+xsqrt(1-y^2)=1," prove that "(dy)/(dx)= - sqrt((1-y^2)/(1-x^2))dot

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

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

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

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