" If "y=(1)/(2)log([1=sin2x," 1"])" prove that "(dy)/(dx)=2" eosee "2x

If y,=(1)/(2)log((1-cos2x)/(1+cos2x)), prove that (dy)/(dx),=2cos ec2x

y=(1)/(2)log((1-cos2x)/(1+cos2x)), prove that (dy)/(dx)=2csc2x

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

If y=(1-tanx)/(1+tanx) , prove that (dy)/(dx)=(-2)/(1+sin2x) .

If y = sin(log_(e) x) prove that (dy)/(dx) = sqrt(1-y^2)/x

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

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