Allow me to make one thing clear - I do not care whether or not My New calculus is published on Wikipedia. No one takes Wikipedia seriously anyway. I discussed it because I was asked. In fact I have been discussing the topic of infinitesimals and kept returning to the topic. Besides, what's preventing you from deleting all these edits? I expect that's exactly what will happen eventually.

Your assertion that the statement  is true only whenever the right hand side exists is false. This statement refers to symbolic derivatives and of course both sides must exist for it to be true, not only the right hand side. The propositional logic applies both ways, that is, given f' + g', it must be true that it equals (f+g)' and vice versa.
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