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That is correct. "(X+X+X……..Xtimes)" is a function! If you are going to evaluate it first, then you have to evaluate the other side too.
The fallacy is that you are differentiating wrt x, but your function is not definded until x itself is defined, but then x will be a constant. Moreover: in d/dX (X+X+X……..Xtimes) the "function" in the brackets is NOT defined at the time of differentiation and so cannot be differentiated.
I have a problem related to derivatives....Please email me the solution, if possible