It would help me understand if you gave an example input/output pair so I
could see what you were wanting to do. I did look at the gist but didn't see
the output that you wanted. Would idiff be of any use?
>>> help(idiff)
Help on function idiff in module sympy.geometry.util:
idiff(eq, y, x, dep=None)
Return dy/dx assuming that y and any other variables given in dep
depend on x.
>>> from sympy.abc import x, y, a
>>> from sympy.geometry.util import idiff
>>> idiff(x**2 + y**2 - 4, y, x)
-x/y
>>> idiff(x + a + y, y, x)
-1
>>> idiff(x + a + y, y, x, [a])
-D(a, x) - 1
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