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'We know that the derivative of x^2 with respect to x is 2x. However, what if we rewrite x^2 as the sum of x x's, and then take the derivative:

d/dx[ x^2 ] = 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 shows that the derivative of x^2 with respect to x is actually x. So what's going on here?'

Wheres the mistake? :P