Extract all instances of variables matching a pattern?

Question

There is a very convenient function Dt that allows to take a total differential of any expression, e.g.:

expr = (a + b c)/d;
Dt[expr]

(Dt[a] + c Dt[b] + b Dt[c])/d - ((a + b c) Dt[d])/d^2

Consider a case where expr is generic (it is not known a priori which and how many variables appear). I would like to have a function that extracts a list of all Dt[x_] from an expression. For the above example it should do:

extract[Dt[expr]]

{Dt[a],Dt[b],Dt[c],Dt[d]}

My own version of this function is:

extract[x_] := Select[Variables[x], (Head[#] === Dt) &]

but I feel like extracting all variables and then selecting a subset is too hacky. Is there a nice way to implement this?

EDIT

Bob Hanlon and Mr. Wizard suggested to use Cases and Union. Unfortunately, these functions appear to be slower than the above in some cases:

Select[Variables[ Dt[(a + b c)/d + (a + b c)/d q]], (Head[#] === Dt) &] // AbsoluteTiming

{0.0000811731, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q]}}

compared to

Cases[Dt[(a + b c)/d + (a + b c)/d q], _Dt, {-2}] // Union // AbsoluteTiming

{0.000136221, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q]}}

Answer 1

Of the various methods proposed in comments, plus a hybrid, I find my proposal fastest:

foo = Dt[(a + b c)/d + (a + b c)/d q + ((a + b c)/d + (a + b c)/d q)/z + 
    q r ((a + b c)/d + (a + b c)/d q + ((a + b c)/d + (a + b c)/d q)/z)];

Select[Variables @ foo, (Head[#] === Dt) &]      // RepeatedTiming

Cases[foo, _Dt, Infinity] // Union               // RepeatedTiming

foo // Variables // Cases[_Dt]                   // RepeatedTiming

Union@Cases[foo, HoldPattern[Dt[_]], Infinity]   // RepeatedTiming

Cases[foo, _Dt, {-2}] // Union                   // RepeatedTiming

{0.0000269, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]}}

{0.00002049, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]}}

{0.000019798, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]}}

{0.00001882, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]}}

{0.0000145, {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]}}

Answer 2

foo = 
Dt[(a + b c)/d + (a + b c)/d q + ((a + b c)/d + (a + b c)/d q)/z + 
 q r ((a + b c)/d + (a + b c)/d q + ((a + b c)/d + (a + b c)/d q)/
     z)];

Union@Level[foo, {-2}] // Cases[#, _Dt] &
(* {Dt[a], Dt[b], Dt[c], Dt[d], Dt[q], Dt[r], Dt[z]} *)

or

Select[Union@Level[expr, {-2}], (Head@# === Dt)&]