Topics:

  • limit definition of the derivative (slope of tangent line at $x=a$):
    • $\displaystyle f’(a) = \lim_{h\to 0}\dfrac{f(a+h)-f(a)}{h}$
  • alternate definition (slope of tangent line at $x=a$):
    • $\displaystyle f’(a) = \lim_{x\to a}\dfrac{f(x)-f(a)}{x-a}$
  • function definition (derivative as a function):
    • $\displaystyle f’(x) = \lim_{h\to 0}\dfrac{f(x+h)-f(x)}{h}$

notes (pdf)