[math]f'(x)=lim_{x\longrightarrow x_0}\left(\frac{f(x)-f(x_0)}{x-x_0}\right))[/math][br]

[math]f'(x)=lim_{x\longrightarrow x_0}\left(\frac{3x^2+2x-\left(3x_0^2+2x_0\right)}{x-x_0}\right)[/math]

[math]3x^2+2x-\left(3x_0^2+2x_0\right)[/math][br][math]=3\left(x^2-x_0^2\right)+2\left(x-x_0\right)[/math][br][math]=3\left(x+x_0\right)\left(x-x_0\right)+2\left(x-x_0\right)[/math][br][math]=\left(x-x_0\right)\cdot\left(3\left(x+x_0\right)+2\right)[/math]

[math]f'(x)=lim_{x\longrightarrow x_0}\left(\frac{3x^2+2x-\left(3x_0^2+2x_0\right)}{x-x_0}\right)[/math][br][math]f'(x)=lim_{x\longrightarrow x_0}\left(\frac{\left(x-x_0\right)\cdot\left(3\left(x+x_0\right)+2\right)}{x-x_0}\right)[/math][br][br][math]=lim_{x\longrightarrow x_0}\left(3\left(x+x_0\right)+2\right)[/math][br][math]=3\cdot2x+2[/math][br][math]=6x+2[/math]