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Is there a way in Mathematica for defining rules for derivatives on undefined functions? For example, I would like to define a rule such that for any function $f(x,y)$, when I take the $x$-derivative it gives me a function $\delta f$:

D[f[x,y],x] -> δf[x,y]
D[g[x,y],x] -> δg[x,y]

etc.

EDIT: I should clarify that I am looking for a rule that could act on functions of any type, so not just $f$, $g$, but any function of $(x,y)$.

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  • $\begingroup$ Do you really want to create a new symbol with a $\delta$ in front, or do you just want to display $f^{(1,0)}$ as $\delta f$? $\endgroup$
    – Lukas Lang
    Aug 5, 2019 at 10:14

1 Answer 1

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Just use Derivative:

f /: Derivative[1,0][f] = 𝛿f;
f /: Derivative[0,1][f] = 𝛿g;

Then:

D[f[x, y], x]
D[f[x, y], y]

𝛿f[x, y]

𝛿g[x, y]

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  • $\begingroup$ I should clarify that I am looking for a rule that could act on functions of any type, so not just f,g, but any function of [x,y]. So the rule would append $\delta$ to any function where I take $\partial_x$. $\endgroup$
    – physics_researcher
    Aug 3, 2019 at 16:41

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