dy/dx can be either +1 or -1.
we know cos-1 (cosx)=x ,(pi+x),-x,(-pi-x) depending on the value of x.here we dont know anything about x.(more precisely alpha-x)
using basic trigo)we get y=cos-1(cos *(alpha-x) or cos-1cos(x-alpha)=alpha -x ,x-alpha etc .etc as above.
here alpha= tan-1(3/2)
on diffrentating we get dy/dx=+1 or -1 (.: alpha is a constant)