Clear[f,df, ddf, x,y]
f[x_,y_]=E^Sin[50 x] + Sin[ 60 E^y] +Sin[70 Sin[x]]+Sin[Sin[80 y]]- Sin[ 10(x+y)]+ ((x^2)+(y^2))/4;
df[x_,y_]=D[f[x,y],{{x,y}}];
ddf[x_,y_]=D[df[x,y],{{x,y}}];
F[]={0,0,0};
F[n_]=Switch[n,
0,F[]=F[]+{1,0,0}; f[x,y],
1,F[]=F[]+{0,1,0}; df[x,y],
2, F[]=F[]+{0,0,1};ddf[x,y]
]

?Substitute

Clear[f]
F[1]

f[x,y]

?Switch

?DynamicModule

?OptionalAr

f[]=12
Information[f]

Clear[f,x]
f[]=0;
f[x_List]:=Module[
{x1,x2},
f[]=f[]+1;
(* fCounter=fCount+1; *)
{x1,x2}=x;
Sin[x1 x2]
]

Information[f]

f[{2.1,3.3}]
f[]

Clear[f]
(Subscript[f, count])

n=0;
ContourPlot[f[x,y],{x,-1,1},{y,-1,1},
PlotLabel->StringForm["`` Evaluations",n]
]

$ModuleNumber

n=0;
ContourPlot[f[{x,y}],{x,-4,4},{y,-4,4},
PlotLabel->StringForm["`` Evaluations",n]
]

n=0;
NMinimize[f[{x,y}],{x,y}
]

Clear[x,y]
Df[{x_,y_}]={D[f[{x,y}],x],D[f[{x,y}],y]}
GradVec=Df[{0.7501393994633998,0.6776482008689373}]

Clear[DDf,x,y]
DDf[{x_,y_}]={D[Df[{x,y}],x],D[Df[{x,y}],y]}
HessianMatrix=DDf[{0.7501393994633998,0.6776482008689373}]

Eigensystem[HessianMatrix]