m[x_, y_] = D[f[x, y], x];
n[x_, y_] =  D[f[x, y], y];
Field[x_, y_] = {m[x, y], n[x, y]};

vectorfieldplot = Table[Vector[gradf[x, y], Tail -> {x, y}, ScaleFactor -> scalefactor], {x, -2, 2, 0.5}, {y, -2, 2, 0.5}];
Show[vectorfieldplot, Axes -> True, AxesLabel -> {"x", "y"}];
{a, b} = {.5, -1};
starterpoint = {a, b};
Clear[x, y, t];
equationx = x'[t] == m[x[t], y[t]];
equationy = y'[t] == n[x[t], y[t]];
starterx = x[0] == a;
startery = y[0] == b;
endtime = 50;
approxsolutions = NDSolve[{equationx, equationy, starterx, startery}, {x[t], y[t]}, {t, 0, endtime}];
Clear[trajectory];
trajectory[t_] = {x[t] /. approxsolutions[[1]], y[t] /. approxsolutions[[1]]};
trajectoryplot = ParametricPlot[trajectory[t], {t, 0, endtime}, PlotStyle -> {{Red, Thickness[0.015]}}];
starterplot = Graphics[{Red, PointSize[0.06], Point[starterpoint]}];
Show[vectorfieldplot, starterplot, trajectoryplot, Axes -> True, AxesLabel -> {"x", "y"}, PlotRange -> All]