Topics:

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

notes (pdf)