Adding a textfield to the function that I implemented

Question

Adding a textfield to the function that I implemented to represent the tangent or derivative of a function, but I've added so mark errors.

f[x_] = -x^3 + 12 x - 3;   (*Se define la función*)
xmin = -6;
xmax = 6 ;     (* se define el mínimo y el máximo de la función*) 
ainicia = -3 ;(* inicio del punto de tangencia*)
amin = -4.3;
amax = 5; (* se define el punto de tangencia mínimo y máximo*)
hinicia = -1;(*inicio del punto de intersección de la línea secante*)
hmin = -1.3;
hmax = 8.5;

Manipulate[
  DynamicModule[{f = Sin[x^2]}, 
  Column[{InputField[Dynamic[f]], Dynamic[Plot[f, {x, -5, 5}]]}]]
  If[h == 0, h = .001];
   Grid[
     {{Plot[{f[x], If[t1, f[a] + (D[f[t], t] /. t -> a)*(x - a)], 
     f[a] + ((f[a + h] - f[a])/h)*(x - a)}, {x, xmin, xmax}, 
     PlotStyle -> {{Thickness[0.005], Black}, {Thickness[0.004], 
     Blue}, {Thickness[0.004], Red}}, 
     PlotRange -> {15*xmin, (8*xmax) + 2}, ImageSize -> {475, 325}, 
     PlotLabel -> Style[Row[{Style["f(x)", Italic], "=",
     ToString[-x^3 + x^2 + 12 x - 3, TraditionalForm]}], 20],
     AxesLabel -> {Style["x", 16, Italic], Style["y", 16, Italic]},
     Prolog -> {{PointSize[0.02], If[t1, Blue, Red], Point[{a, f[a]}]},
      {PointSize[0.02], Red, Point[{a + h, f[a + h]}]}}]},
      {Row[ 
       {If[t1, 
       Style[Text[
      "Pendiente-tangente =" <> ToString[D[f[t], t] /. t -> a]], 
      Blue, 20]],
     Style[
     Text["Pendiente-secante =" <> ToString[(f[a + h] - f[a])/h]], 
     Red, 20]}, "   "]}}],
     {{a, ainicia, "x0"}, amin, amax},
      {{h, hinicia, "h"}, hmin, hmax},
      {{t1, False, "Linea Tangente"}, {True, False}},
      TrackedSymbols -> {a, h, t1}, SaveDefinitions -> True]

I do not like putting the textfield to enter the function, which is shown in the graph and is the same for the tangent.

Answer 1

Basically, you're trying to do this:

Manipulate[
 Plot[func, {x, -10, 10}],
 {func, x^2}]

You can add that field to your application but use the symbol f instead of func and it will work for input such as Sin, Exp etc. However it will not work for input such as x^2. This is because you use f[t] and so on instead of the expression itself (Sin is a function but x^2 is just an expression).

To make it work this way you need to stop using functions such as f[t] and simply use f instead where f is not used as a function anywhere, but is assumed to be an expression (such as x^2).