differentiate x + 1/x from first principle

Let y = x + 1xy + y = x+x + 1x+xy =  x+x + 1x+x - yy =  x+x + 1x+x - x - 1xy = x + 1x+x - 1xy = x + x-x-xxx+xyx = xx - xx×1xx+xyx = 1 - 1xx+xlimx0yx = limx01 - 1xx+xdydx = 1 - 1x2

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