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

If y=log sqrt((1-tan x)/(1+tan x)), prove that (dy)/(dx)=sec2x

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

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

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

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