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A nice one...


sage: R.<x>=InfinitePolynomialRing(QQ)
sage: f=R(x[1]^3)

Note that :

sage: [u.parent() for u in f.variables()]
[Multivariate Polynomial Ring in x_2, x_1, x_0 over Rational Field]

(yes, I played with R a bit...) contrasting with:

sage: x[1].parent()
Infinite polynomial ring in x over Rational Field

Hence the error you noticed. However :

sage: x[1] in f.variables()

It is there ; you just have to find it :

sage: f.variables().index(x[1])

Hence the (awkward) :

sage: f.derivative(f.variables()[f.variables().index(x[1])])

A better way would be to cast x[1] to the proper class. Finding which isn't intuitive...