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 whats preventing you from deleting all these edits I expect thats 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 fg and vice versa