We know $x.x=x^2$(Consider $x\ne 0$)

$x.x$ is adding $x$ $x$ times. So we have

$x+x+\dots+x$($x$ times $x$ is added)=$x^2$......(1)

Differentiating both sides of (1) we get,

$1+1+\dots+1$(x times)=$2.x$

$\Rightarrow x=2x$

$1=2$ Proved.

Find out the mistake in this proof.