Вот решение, если кому надо будет
Код:
ClearAll[x, y, F, g]
F[x_, y_] := Sin[x]/Sqrt[x] + Cos[Sqrt[y]]/ArcTan[y]
g[x_, y_] = Grad[F[x, y], {x, y}]
Manipulate[
Show[#, # /. p : {_Real, _Real} :> p + t g @@ p /. Blue -> Red] &@
ContourPlot[F[x, y] == 0, {x, 1, 20}, {y, 0, 10},
BaseStyle -> {Thickness@.01}, ContourStyle -> Blue], {t, 0, 5}]