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

d/dx x^2 = d/dx [x + x + ... + x] 

2x = x

2 = 1

 

Enjoy. Now, can you find the problem?

Yes.

2 = 1 is false.

If you take x from both sides, you get:

2 = 0

So it should be proving 2 = 0, not 2 = 1.

1 hour ago, ydoaPs said:

frax{d}{dx}

Is this bit at fault?

12 minutes ago, studiot said:

Is this bit at fault?

Yeah, as far as I can tell, it's because x is being treated like a constant instead of a function on the right hand side in the first step.