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

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

lf y=sqrt((1-x)/(1+x)) find dy/dx and prove that (1-x^2)(dy)/(dx)+y=0

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

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

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

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

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

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

If y = (sin^-1x)/(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)