Take logs of each side:
ln|y|=2ln|sin(x)|+4ln|tan(x)|-2ln|x2+1|, and differentiate:
(1/y)(dy/dx)=2cos(x)/sin(x)+4sec2(x)/tan(x)-4x/(x2+1)=
2cot(x)+4sec(x)csc(x)-4x/(x2+1).
dy/dx=(2cot(x)+4sec(x)csc(x)-4x/(x2+1))sin2(x)tan4(x)/(x2+1)2, substituting for y.
dy/dx=tan4(x)(sin(2x)+4tan(x))/(x2+1)2-4x/(x2+1)3 (for example).