Quiet@Remove["Global`*"];
$HistoryLength=2;
SetDirectory[NotebookDirectory[]];

(*example 1*)
exp=(x^2)+x*y+(y^2);
{0==D[exp,x],0==D[exp,y]}//Solve

constrainFunction=2(x^2)+3(y^2)-5;
ContourPlot[constrainFunction==0,{x,-3,3},{y,-3,3}];

lagrangeFunction=exp+λ*constrainFunction;
sols=({0.==D[lagrangeFunction,x],0.==D[lagrangeFunction,y],0.==D[lagrangeFunction,λ]}//Solve)

{exp/.#,#}&/@sols

(((10^21)*0.001)/(3600*24*356))

Quiet@Remove["Global`*"];
SetDirectory[NotebookDirectory[]];

Normal[Series[f[x],{x,x0,3}]]/.{x->x0+Δx}
Normal[Series[f[x],{x,x0,3}]]/.{x->x0-Δx}
%%-%

f:=Sin;
Δx=0.1;
der1[x_]:=((f[x+Δx]-f[x])/(Δx));
der2[x_]:=((f[x+Δx]-f[x-Δx])/(2*Δx));
Plot[{f'[x]-der1[x],f'[x]-der2[x]},{x,0,2Pi},AxesLabel->{"x","err1 err2 "},PlotStyle->{{Red,Thick},{Blue,Thick}},PlotLabel->"Δx= "<>ToString[Δx]]