# Plot Derivative of ODE system

I want to Plot Derivatives of ODE system.

n = 10;
T = 20;
r = 1.4;
A1 = 1;
A2 = 0.01;
RPT = 5;
IC = Table[RandomReal[{$MachineEpsilon, 1}, n], {j, RPT}]; eqns = Table[{x[i]'[t] == x[i][t] (r - A1 x[i][t] - (Sum[A2 x[k][t] Boole[i != k], {k, n}]) ), x[i][0] == IC[[j]]}, {j, RPT}, {i, n}]; vars = Table[x[i][t], {j, RPT}, {i, n}]; vars2 = Table[Derivative[x[i][t], t], {j, RPT}, {i, n}] sol = Table[NDSolve[eqns[[j]], vars[[j]], {t, 0, T}], {j, RPT}]; Table[Plot[Evaluate[vars[[j]] /. sol[[j, 1]]], {t, 0, T}, PlotRange -> All, PlotStyle -> Automatic], {j, RPT}]  The graph of the derivative does not work well. Table[Plot[Evaluate[vars2[[j]] /. sol[[j, 1]]], {t, 0, T}, PlotRange -> All, PlotStyle -> Automatic], {j, RPT}]  Can anybody help me? • Definition of vars2 is apparently wrong, Derivative[x[i][t], t] just doesn't make sense. – xzczd Feb 9 at 9:05 ## 1 Answer It is necessary to separate the components of the solution, for example n = 10; T = 20; r = 1.4; A1 = 1; A2 = 0.01; RPT = 5; IC = Table[RandomReal[{$MachineEpsilon, 1}, n], {j, RPT}];
eqns = Table[{x[j][i]'[t] ==
x[j][i][t] (r -
A1 x[j][i][t] - (Sum[A2 x[j][k][t] Boole[i != k], {k, n}])),
x[j][i][0] == IC[[j]]}, {j, RPT}, {i, n}];
vars = Table[x[j][i][t], {j, RPT}, {i, n}];
vars2 = Table[D[x[j][i][t], t], {j, RPT}, {i, n}];

sol = NDSolve[eqns, vars, {t, 0, T}];
sol2 = NDSolve[eqns, vars2, {t, 0, T}];

Table[Plot[Evaluate[vars[[j]] /. sol], {t, 0, T}, PlotRange -> All,
PlotStyle -> Automatic], {j, RPT}]
Table[Plot[Evaluate[vars2[[j]] /. sol2], {t, 0, T}, PlotRange -> All,
PlotStyle -> Automatic], {j, RPT}]