Clear[x];
x[t_]:={3(t^3)-5(t^2)+2,-0.5(t^3)+2(t^2)-3t+1,1.5(t^3)-2};

MatrixForm[x[t]]

xvals=Table[x[t],{t,-5,5,0.01}];

xvals[[1;;10]]

Graphics3D[{Thick,ColorData[97,"ColorList"][[1]],Line[xvals]},Boxed->False,Axes->True,AxesOrigin->{0,0,0},PlotRange->{{-5,5},{-5,5},{-5,5}},AxesLabel->{"x","y","z"},ImageSize->Large,BaseStyle->{FontSize->14}]

Clear[Dert];
Dert=D[x[t],t]

Dert/.{t->0}

Graphics3D[{
{Thick,ColorData[97,"ColorList"][[1]],Line[xvals]},
 {PointSize[0.01],ColorData[97,"ColorList"][[1]],Point[x[0]]},
 {PointSize[0.01],ColorData[97,"ColorList"][[1]],Arrow[{x[0],x[0]+(Dert/.{t->0})}]}},
Boxed->False,Axes->True,AxesOrigin->{0,0,0},PlotRange->{{-5,5},{-5,5},{-5,5}},AxesLabel->{"x","y","z"},ImageSize->Large,BaseStyle->{FontSize->14}]