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I guess what you are looking for is something like this scalefactor = 0.5; P[t_] = {t Sin[t], t^2/15}; curveplot[t0_] := ParametricPlot[P[t], {t, 0, t0}, PlotStyle -> Thickness[0.01], AxesLabel -> {"x", "y"}] vel[t_] = D[P[t], t]; velvector[t0_] := Graphics[{Red, Arrow[{P[t0], P[t0] + scalefactor vel[t0]}]}] Manipulate[Show[...



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