Day 21 in Mat121

Today:

• This Friday the first Mathematics Majors (and minors) Lunch will be held, from 11:30am to 1:30pm, in ST 343. Come even if you're just thinking about majoring or minoring in math. Heckle and provoke your professors, no extra charge!

• Don't forget: exam 2 Thursday, over derivatives (through 3.7).

• Quiz today (derivatives)

• Hand out directed reading handout, Section 3.8 (html) (pdf)

• Section 3.7: The Chain Rule
  • The Chain Rule:

    Given a composition

    identify
    • The outside function: f(stuff), where
    • stuff (=g(x)) is all the rest of the stuff; then
    • calculate f'(stuff), where the derivative is wrt (with respect to) stuff, and
    • calculate stuff'(x)
    Note that stuff may itself require use of the chain rule. This is an iterative process, like a lot of mathematics: doing the same thing over and over and over again....

    Then clean up your stuff: replace the stuff you introduced into this problem in terms of x (stuff=g(x)):

  • Motivation from the limit definition of the derivative.

  • Someone needs to make a chain rule song out of The Pretenders' "Back on the Chain Gang".
    • Back on the Chain Gang, lyrics and chords
    • Pretenders live
    • The music video

  • Examples:
    • Preliminary questions 1-4, p. 152
    • #21-50, inner and outer, p. 153
      • #29
      • #37
      • #41
    • #68, p. 153

  • Questions over the Directed reading handout, Section 3.7 (html) (pdf)?

• Links:
  • Calculus Christmas Carols
  • Great calculus demos (and more on the chain rule).