Comment by OlleTO

Proof: The derivative of x^2 is x.

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

Therefore,

d/dx(x^2) =

d/dx(x * x) =

d/dx (x + x + ... + x (x times)) =

d/dx(x) + d/dx(x) + ... + d/dx(x) (x times) =

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

x