Small question about the output form of the derivative

Question

I have an expression:

D[D[Subscript[T, 1][x[t], y[t], x'[t]] + Subscript[T, 2][x[t], y[t], y'[t]], x'[t]], t]

The result is:

$y'(t) T_1{}^{(0,1,1)}\left(x(t),y(t),x'(t)\right)+x'(t) T_1{}^{(1,0,1)}\left(x(t),y(t),x'(t)\right)+x''(t) T_1{}^{(0,0,2)}\left(x(t),y(t),x'(t)\right)$

I need to make it so that when differentiating with respect to time, variables $x'(t)$ and $y'(t)$ are not taken out of brackets.

Answer 1

Clear["Global`*"]

Use HoldForm

(expr = HoldForm[
   D[D[Subscript[T, 1][x[t], y[t], x'[t]] + 
      Subscript[T, 2][x[t], y[t], y'[t]], x'[t]], t]])

expr // TraditionalForm

expr // ReleaseHold

EDIT: To reverse the order of the products

expr2 = HoldForm[D[D[f[x[t], y''[t], z''[t], x'[t]], x'[t]], t]]

expr2 // TraditionalForm

expr2r = (expr2 // ReleaseHold) /. Times[a_, b_] :> HoldForm[Times[b, a]]

expr2r // TraditionalForm

EDIT 2: For the revised question

expr3 = Derivative[2][x][t]*
    Derivative[0, 0, 2, 0, 0][f][x[t], y[t], Derivative[1][x][t], 
     Derivative[2][y][t], Derivative[3][z][t]] + 
   Derivative[3][y][t]*
    Derivative[0, 0, 1, 1, 0][f][x[t], y[t], Derivative[1][x][t], 
     Derivative[2][y][t], Derivative[3][z][t]] + 
   Derivative[1][y][t]*
    Derivative[0, 1, 1, 0, 0][f][x[t], y[t], Derivative[1][x][t], 
     Derivative[2][y][t], Derivative[3][z][t]] + 
   Derivative[1, 0, 0, 0, 0][f][x[t], y[t], Derivative[1][x][t], 
    Derivative[2][y][t], Derivative[3][z][t]] + 
   Derivative[4][z][t]*
    Derivative[0, 0, 1, 0, 1][f][x[t], y[t], Derivative[1][x][t], 
     Derivative[2][y][t], Derivative[3][z][t]] + 
   Derivative[1][x][t]*
    Derivative[1, 0, 1, 0, 0][f][x[t], y[t], Derivative[1][x][t], 
     Derivative[2][y][t], Derivative[3][z][t]];

(expr3r = expr3 /. Plus :> Inactive[Plus] /.
    Inactive[Plus][a__, b_, c_] :> Inactive[Plus][a, c, b]) // 
      TraditionalForm

For subsequent operations Activate expr3r