Plotting Tangent Lines

cubic[x_] := (x^3-2x^2 -2 x + 1)/8;
quartic[x_] := 1+(x^4 + 3 x^3 - 20 x^2 + x + 3)/100;
g[x_] := Sin[x];
h[x_] := x^3;
chain[x_] := h[g[x]];
bad[x_] := If[x≠ 0, x Sin[1/x],0];
Manipulate[Plot[{f[x], f[x1]+f'[x1]*(x-x1)},{x,-c, c},PlotRange -> {-r,r}, Epilog -> {PointSize[.025], Point[{x1,f[x1]}]}],{x1,-c, c}, {c, 2 Pi, 0},{r,3,.001},{f, {Sin,Cos,Tan,Sec,Csc,Cot,Exp,cubic,quartic,g,h,chain,bad}}]

c=2;
Exp[-((x-1.2)^2+(y-1.2)^2)/.4] ;
ff[x_,y_] := (x^2+y^2)^2-4(x^2+y^2);
Exp[-(x^2+y^2)/.4] ;
ff[x_,y_] := Exp[-(x^2+y^2)/.4] + .5  Sin[2y x];Manipulate[Plot3D[{ff[x,y], If[Abs[x-x1] ≤ c/3 && Abs[y-y1] ≤ c/3,ff[x1,y1]+(D[ff[u,y1],u] /. u->x1)*(x-x1) + (D[ff[x1,v],v] /. v->y1)*(y-y1),ff[x,y]] },{x,-c, c},{y,-c,c}, PlotRange -> {-r,r}],{x1,-c,c},{y1,-c,c}, {r,2,.10}]

ff[x_,y_] := If[x^2 + y^2 > 0,x^(1/3) y^(1/3),0];
Plot3D[x^(1/3) y^(1/3),{x,0,1},{y,0,1}]
Manipulate[Plot3D[{ff[x,y], If[Abs[x-x1] ≤ c/3 && Abs[y-y1] ≤ c/3,(ff[x1,y1]+(D[ff[u,y1],u] /. u->x1)*(x-x1) + (D[ff[x1,v],v] /. v->y1)*(y-y1))] },{x,r, c},{y,r,c},PlotRange -> {0,h}], {r,.1,.0001},{c,.2,r}, {x1,r,c},{y1,r,c},{h,1,.001}]