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Instead of "assigning" a value to g/x|x=0 beforehand, it's easier to make the substitution afterward:

sage: der_f.subs(x==0).subs(diff(g,x).subs(x==0) == 10)
12
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Instead of "assigning" a value to g/x|x=0 beforehand, it's easier to make the substitution afterward:

sage: der_f.subs(x==0).subs(diff(g,x).subs(x==0) == 10)
12

Or in steps, mimicking the order you proposed:

sage: what_i_know = diff(g,x).subs(x==0) == 10
sage: der_f.subs(x==0).subs(what_i_know)
12