Day 15 in Mat121

Today:

• Roll

• The Learning Assistance Center is waiting for you!

• directed reading handout, Sections 3.2 and 3.3 (html) (pdf)

• Sections 3.2 and 3.3: The Derivative Function, and important rules
  • The definition

  • Examples, using the definition
    • From last time:
    • #6, p. 116

    • Derivatives of constant functions and the function f(x)=x

  • Rules that help us avoid the definition! (with Proofs)

    • The sum rule

      works as we'd hope: the derivative of a sum is the sum of the derivatives

    • The power rule (via dominoes -- i.e., mathematical induction)

    • The constant multiple rule (makes sense)

    • NOTE: at this point we have all the rules necessary to differentiate all polynomials, without needing to resort to the definition!

    • The product rule

      Rats! "The derivative of the product is not the product of the derivatives."

    • The quotient rule (Rats again!)

  • #63 and 64, p. 118