Weird Proof Involving Derivatives

Here is a "proof" that if x² = x(x), then 1 = 2 as well:

• x² = x(x)
• x² = x + x + x + ... + x
• (x²)' = (x + x + x + ... + x)'
• 2x = 1 + 1 + 1 + ... + 1
• 2x = x
• 1 = 2
• QED