Algo rudimentario pero funciona.
f[x_] = ArcTan[x]
f1[x_] = D[f[x], x]
f2[x_] = D[f1[x], x]
f3[x_] = D[f2[x], x]
f4[x_] = D[f3[x], x]
f5[x_] = D[f4[x], x]
P[z_, x_] =
f[x] + f1[x]*(z - x) + f2[x]/2*(z - x)^2 + f3[x]/6*(z - x)^3 +
f4[x]/24*(z - x)^4 + f5[x]/120*(z - x)^5;
P[x, 0]
Plot[{f[x], P[x, 0]}, {x, -5, 5}, PlotStyle -> {Black, Blue},
PlotRange -> {-5, 5}]