### Quiz 3.2:

Question:

Use the definition of the derivative function to find $$\frac{dy}{dx}$$ for $$y=2x^3$$

Solution:

$$\frac{dy}{dx} = \lim \limits _{h \rightarrow 0} \frac{2(x+h)^3-2x^3}{h}=\lim \limits _{h \rightarrow 0} \frac{2x^3+6x^2h+6xh^2+2h^3-2x^3}{h}=\lim \limits _{h \rightarrow 0} \frac{6x^2h+6xh^2+2h^3}{h}=\lim \limits _{h \rightarrow 0} 6x^2+6xh+2h^2=6x^2$$