(a) y=6x-(2/x), dy/dx=6+(2/x2)
(b) y=x/(x+1); u=x, v=(x+1)-1, dy/dx=udv/dx+vdu/dx=-x/(x+1)2+1/(x+1)=(-x+x+1)/(x+1)2=1/(x+1)2; or, u=x, v=x+1, dy/dx=(vdu/dx-udv/dx)/v2=(x+1-x)/(x+1)2=1/(x+1)2
(c) y=-x, dy/dx=-1
(d) y=10log|x|, dy/dx=10/x if log is natural log ln (that is, loge)
(e) y=√(16x)=4√x=4x½, dy/dx=2/√x the same as 2√x/x