I presume that, y=(cosx+sinx)/(cosx-sinx),
={cosx(1+sinx/cosx)}/{cosx(1-sinx/cosx)},
=(1+tanx)/(1-tanx),
rArr y=tan(pi/4+x)
:. dy/dx=sec^2(pi/4+x)*d/dx(pi/4+x)..."[The Chain Rule]",
=sec^2(pi/4+x).
Also, dy/dx=1/cos^2(pi/4+x),
=1/(cos(pi/4+x))^2,
=1/(cos(pi/4)cosx-sin(pi/4)sinx)^2,
=1/(1/sqrt2*cosx-1/sqrt2*sinx)^2.
rArr dy/dx=2/(cosx-sinx)^2, or,
dy/dx=2/(cos^2x-2cosxsinx+sin^2x)=2/(1-sin2x).