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

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= y=sqrt((1-sin 2x )/(1+sin 2 x)) prove that (dy)/(dx)+sec^2(pi/4-x)=0.

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

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

If y=sqrt(1+sqrt(1+x^(4))), prove that y(y^(2)-1)(dy)/(dx)=x^(3)

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

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 .