f[t_]={(3t-1)/(t+6)Sin[t]-1/2,2(t-4)/(t+3)Cos[t]+1}

df[t_] = D[f[t],t];

showderivative=True;

Animate[ParametricPlot[f[tt],{tt,0,10},PlotRange->2,PlotStyle->Thick,Epilog->{PointSize[.03],Red,Point[f[t]], Black,If[showderivative,Arrow[{f[t],f[t]+df[t]}],{}]}], {t,0,10}]