Jika y=3x^2-2x+5, tentukan dy/dx dengan menggunakan definisi

[tex]$\begin{align}y&=f(x)=3x^2-2x+5 \\ \frac{dy}{dx}&=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \\ &=\lim_{h\to 0}\frac{[3(x+h)^2-2(x+h)+5]-[3x^2-2x+5]}{h} \\ &=\lim_{h \to 0}\frac{[3x^2+6xh+3h^2-2x-2h+5-3x^2+2x-5]}{h} \\ &=\lim_{h \to 0}\frac{6xh-2h}{h} \\ &=\lim_{h \to 0}6x-2 \\ &=6x-2\end{align}[/tex]