Wah this discussion still going on arr... See the wiki site on the previous page la... While it's true that
x^2=x+x+x+x+...+x+x (x number of times)
and
d/dx(x^2)=2x,

the mistake is
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (x number of times)
because x here is not held constant.

Of course you can differentiate x^2 and y can equal x. Just that when you make it equal to x, you have to differentiate it as well now.
d/dx(y*x) = d/dx(y)*x + y*d/dx(x) = 0+y = y
and
d/dx(x*x) = d/dx(x)*x + x*d/dx(x) = x+x = 2x

If you follow the example in the first post, you'll be differentiating only one x while there are actually two there. Which means you don't apply the multiplication law.