By definition,
[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]
Let x = 1. Then
[tex]f'(1) = \displaystyle \lim_{h\to0}\frac{f(1+h)-f(1)}h \\\\ f'(1) = \lim_{h\to0}\frac{(3(1+h)^2+2(1+h)+1)-6}h \\\\ f'(1) = \lim_{h\to0}\frac{3+6h+3h^2+2+h+1-6}h \\\\ f'(1) = \lim_{h\to0}\frac{7h+3h^2}h \\\\ f'(1) = \lim_{h\to0}(7+3h) = \boxed{7}[/tex]
