In the code you last posted, you do a substitution of new_var with vi and
then differentiate wrt new_var. This will necessarily give you 0, won't it?
Is this what you are trying to do:
>>> def vdiff(x, vector):
... ans = []
... for vi in vector:
... if vi.is_Symbol:
... tmp = []
... for e in x:
... tmp.append(e.diff(vi))
... else:
... subs = {}
... new_var = Dummy()
... for s in vi.free_symbols:
... subs[s] = solve(new_var - vi, s)[0]
... tmp = []
... for e in x:
... e = e.subs(subs, simultaneous=True)
... d = Dummy('ei')
... e = idiff(d-e, d, new_var)
... e = e.subs({new_var: vi})
... tmp.append(e)
... ans.append(tmp)
... return ans
...
>>> vdiff([x, x+y], [x, x-c])
[[1, 1], [1, 1]]
>>> vdiff([x, x+y], [x, exp(x)-c])
[[1, 1], [exp(-x), exp(-x)]]
>>> vdiff([x, x+y], [x, exp(x)-y])
[[1, 1], [exp(-x), (-exp(x) + 1)*exp(-x)]]
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