Вычислить производную функции по определению.

[latex] \lim_{\text{$\Delta $x} \to 0} \frac{f(x+\text{$\Delta $x})-f(x)}{\text{$\Delta $x}} = \lim_{\text{$\Delta $x} \to0} \frac{(x+\text{$\Delta $x})^2+3-x^2-3}{\text{$\Delta $x}} =\\ = \lim_{\text{$\Delta $x} \to 0} \frac{x^2+2x\text{$\Delta $x}+(\text{$\Delta $x})^2-x^2}{\text{$\Delta $x}}= \lim_{\text{$\Delta $x} \to 0} \frac{\text{$\Delta $x}(2x+\text{$\Delta $x})}{\text{$\Delta $x}}=2x [/latex]