A falsidical paradox

[^ represents to the power of and (d/dx) represents differentiation with respect to x]

x^2 = x + x + ... + x (x times)

=> (d/dx)(x^2) = (d/dx)(x + x + ... + x)

=> 2x = 1 + 1 + ... + 1 (x times)

=> 2x = x

Of course, this is wrong. Find the bug in the argument. Also explain why we are getting '2' particularly.