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![f(x)=6x+2,\ x_0=1\\\\f'(x_0)=\lim\limits_{h\to0}\dfrac{f(x_0+h)-f(x_0)}{h}\\\\f'(1)=\lim\limits_{h\to0}\dfrac{f(1+h)-f(1)}{h}=\lim\limits_{h\to0}\dfrac{6(1+h)+2-[6(1)+2]}{h}\\\\=\lim\limits_{h\to0}\dfrac{(6)(1)+(6)(h)-(6+2)}{h}=\lim\limits_{h\to0}\dfrac{6+6h-8}{h}\\\\=\lim\limits_{h\to0}\dfrac{6h-2}{h}=\lim\limits_{h\to0}\left(\dfrac{6h}{h}-\dfrac{2}{h}\right)=\lim\limits_{h\to0}\left(6-\dfrac{2}{h}\right)=6\\\\\ \boxed{f'(1)=6}](/tpl/images/0096/7729/0be2b.png)
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Find the derivative of f(x) = 6x + 2 at x = 1. 1 2 3 6...
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