Here are the main points that are addressed in the video. Please read these and think about them as you watch.

• The derivative of a function $f$ at an input value $x = a$ is the limit of the average rate of change of $f(x)$ with respect to $x$ over the interval $[a, a + h]$ (assuming $h > 0$) as $h$ approaches zero.
• The derivative of a function $f$ at an input value $x = a$ is given by either of the following expressions:
  • $\lim _{h \to 0} \dfrac {f(a+h)-f(a)}{h}$
  • $\lim _{x \to a} \dfrac {f(x)-f(a)}{x-a}$