" If "y=2tan(x)/(2)," prove that "(dy)/(dx)=(2)/(1+cos x)

If y,=2tan backslash(x)/(2), then prove that (dy)/(dx),=(2)/(1+cos x)

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

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

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

If y = ( tan x)/( 1+ tan^2 x), Prove that (dy)/(dx) = cos 2x.

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

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

if y=tan^(-1)((sin x)/(1+cos x)) prove that (dy)/(dx)=(1)/(2)

if y=tan^(-1)((2x)/(1-x^(2))) then prove that (dy)/(dx)=(2)/(1+x^(2))