Drawing an arrow and manipulating it in a diagram

Question

I want to draw an arrow in a diagram which starts from a point, say, $(x,\,\sqrt{x^2+2})$ and ends up at a point, say, $(x',\,\sin{x^2})$.

I want to manipulate or animate such an arrow. For example, I want to animate how the arrow starting from a point proceeds to the end point. But I don't know how!

Any idea would be appreciated!

Answer 1

But how can I animate the growing of the arrow starting from a point and ending up at another point?

Per comment. This version supports different x for each function.

Manipulate[

 Plot[{g, f}, {x, -10, 10}, PlotLegends -> {"f(x)", "g(x)"}, 
  PlotRange -> {{-5, 5}, {-5, 5}},
  Epilog -> {Arrow[{{xfValue, f /. x -> xfValue}, {xgValue, 
             g /. x -> xgValue}}]}
 ],

 Grid[{
   {Control[{{f, Sqrt[x^2 + 2]}, InputField}]},
   {Control[{{g, Sin[x^2]}, InputField}]}}
 ],

 {{xfValue, 1, "x for f"}, -10, 10, .1, Appearance -> "Labeled"},
 {{xgValue, 4.1, "x for g"}, -10, 10, .1, Appearance -> "Labeled"}
 ]