I found this browsing the net. Any comments?

The derivative of x², with respect to x, is 2x.  However, suppose we write x² as the sum of x x's, and then take the derivative:

Let f(x) = x + x + ... + x  (x times)

Then f'(x) = d/dx[x + x + ... + x]  (x times)
  = d/dx[x] + d/dx[x] + ... + d/dx[x]  (x times)
  = 1 + 1 + ... + 1  (x times)
  = x

This argument appears to show that the derivative of x², with respect to x, is actually x.  Where is the fallacy?