This a tricky math question I encountered. I know a little bit about the answer. But I want somebody who is very good at math to help me find the real reason behind this.

OK

Lets start

$1^2 = 1$

$2^2 = 2+2$

$3^2 = 3+3+3$

...........................

................................

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

Differentiating with respect to $x$

We get

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

which is equal to

$2x = 1*x$

$2x = x$

Which is incorrect.

Where did I go wrong?? :O :O