Use the rule d(u/v)/dx=(vdu/dx-udv/dx)/v^2.
Let u=3-x and v=3+x; du/dx=-1 and dv/dx=1;
derivative of (3-x)/(3+x)=(-3-x-3+x)/(3+x)^2=-6/(3+x)^2.
Let u=ln(x) and v=tan(x); du/dx=1/x and dv/dx=(sec(x))^2;
derivative=(tan(x)/x - (sec(x))^2ln(x))/(tan(x))^2.
dy/dx=-6/(3+x)^2+(tan(x)-x(sec(x))^2ln(x))/(x(tan(x))^2).