I'd like to define specific partial derivative operators that change based on if the passed expression is a function of, for example, x vs. xi. I'm not finding anything in the documentation on how to code a check for the expressions dependence. My question is, if given some function f[x,y], how can I check the variables that it depends on?

  • 3
    $\begingroup$ Possible duplicate of How to define custom differential operator using the arguments of the expression? $\endgroup$
    – Carl Woll
    Sep 5, 2018 at 21:43
  • $\begingroup$ I think it should be possible to also use DownValues[f] to find what the function depends on, since the DownValues has the function signature right there. It just needs to be parsed out and to extract all the symbols from inside f[x_,y_,....] and this part might be tricky to do. ?DownValues $\endgroup$
    – Nasser
    Sep 6, 2018 at 1:50

1 Answer 1


Perhaps Internal`DependsOnQ:

h = f[x, g[y]];
Internal`DependsOnQ[h, #] & /@ {x, y, g[y], w}

{True, True, True, False}


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