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

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

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

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

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

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)=sqrt(x)-(1)/(sqrt(x))

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

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