Manipulate[Plot[{Sin[x], (∑_(n=0)^d)((((-1))^n)/((2n+1)!))x^(2n+1)}, {x, -30, 30}, PlotRange -> {-10,10}, AspectRatio -> 1, PlotStyle -> {{Thick, Blue}, {Thick, Red}}], {d, 0,100, 1}]

Manipulate[Plot[{E^x, (∑_(n=0)^d)((x^n)/((n)!))}, {x, -30, 8}, PlotRange -> {-10,10}, AspectRatio -> 1, PlotStyle -> {{Thick, Blue}, {Thick, Red}}], {d, 0,100, 1}]