![\bf \textit{de}\textit{finition of a derivative as a limit}\\\\ \lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}\\\\ -------------------------------\\\\ f(x)=5x^2-6x-3 \\\\\\ \lim\limits_{h\to 0}~\cfrac{[5(x+h)^2-6(x+h)-3]~~-~~(5x^2-6x-3)}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{[5(x^2+2xh+h^2)-6(x+h)-3]~~-~~5x^2+6x+3}{h}](/tpl/images/0252/8215/0d275.png)
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