If `y=sqrt[(1-cosx)/2]` then prove that `dy/dx = 1/2cos(x/2)`.

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

If y=(sin x)/(1+cos x) then prove that (dy)/(dx)=(1)/(1+cosx)

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

If y=sqrt(cos x+sqrt(cos x +sqrt(cos x+....oo))) " then prove that " dy/dx = sinx /(1-2y).

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

If y=sqrt(sin x+sqrt(sin x +sqrt(sin x+....oo))) " then prove that " dy/dx = cos x /(2y-1).

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

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