Bhrasta Kangressi,

I am surprised that all you could come up with is that trivial question. I thought you would ask something harder, like whether I remember the proof of uniform limit of continuous function is continuous or something like that. The question you asked is so trivial that it only exposes your inadequacy. And no it was not your typo. Anybody who has read your postings over time knows how dumb and stupid you are and yet how unaware you are of your own weakness.

To answer your question, the derivatives are always calculated by using limit argument. Take the value of the function, in this case x^2, at x and its neighborhood, x+h, and calculate the difference. Divide it by h. Now take a limit of h->0. You got your derivative. Since x^2 is a polynomial (quadratic) function, you know its derivative exists everywhere. But suppose say you are in a shaky territory. Then it is important to take both right and left limit, and proove that they are equal. If they are equal, then this limit value is the derivative. If they are not equal, the derivative doesn't exist at the point.