\(\eqalign{
& y'({x_0}) = \mathop {\lim }\limits_{x \to {x_0}} {{{x^2} - {x_0}^2} \over {x - {x_0}}} = \mathop {\lim }\limits_{x \to {x_0}} {{(x - {x_0})(x + {x_0})} \over {x - {x_0}}} \cr
& = \mathop {\lim }\limits_{x \to {x_0}} (x + {x_0}) = 2{x_0} \cr} \)
