How to convert a multivariable polynomial with integer coefficients to one with Float64 coefficients?

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Conversion can be done with convert:

using DynamicPolynomials
@polyvar x[1:3]
m = monomials(x, 0:3)
mD = differentiate.(m, x[1]) * 1.0
mD2 = convert.(Term{true, Float64}, differentiate.(m, x[1]))
mD2 == mD
true

This can be easily seen in the source code:

If you want to be comfortable, you should also take a look at the source code.