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According to first principles, the differential is found as the limit as h->0 of:[f(x+h)-f(x)] / hif we set our f to x^2, then we find that this expression becomes (x^2+2hx+h^2 - x^2)/hWhich simplifies to 2x+h. As h->0, this leaves us with 2x, which is the derivative of x^2