z[t_]:=Exp[((-(t^2))/2)];
D[z[t],t]
Simplify[D[z[t],{t,2}]]
Simplify[D[z[t],{t,3}]]
Simplify[D[z[t],{t,4}]]
Simplify[D[z[t],{t,5}]]
Simplify[D[z[t],{t,6}]]