Warm up dealt with product rule in the application of writing a tangent line equation. Worked through finding the derivative of tan(x), added it to our booklets. I gave you the other derivative rules, and made a big mistake!! Sorry. See the linked notes for the correction. Here is what should be in your booklets (secant and cosecant were wrong on the board).
Homework
p. 105 #75-80 (determine differentiability graphically), 87-90 (determine algebraically)
p. 125 #3-33 (multiples of 3)
Resources
determining differentiability from a graph: link
determining differentiability algebraically: link
product rule examples: link
quotient rule examples: link
Warm up dealt with another tangent line equation problem, this time dealing with the quotient rule and the derivative of the tan function. Went over homework, corrected the trig derivative mistake I made last time and actually found the derivative of secant using the quotient rule. Introduced the chain rule, which is used when taking the derivative of composite functions, where one function is nested in another. Analogies of "party and after party" and "Russian nesting dolls" to explain the procedure of composite derivatives. (Here is some intuition on the chain rule if interested: LINK). Worked through several examples, including one using the chain rule twice and an AP multiple choice problem.
Notes from board
Homework
this handout: any 5 problems from #1-10, any 8 problems from #451-67.
Resources
simple chain rule examples: https://www.youtube.com/watch?v=6kScLENCXLg
more chain rule examples: https://www.youtube.com/watch?v=6_lmiPDedsY
Warm up was a guided example on how to find values to make a function differentiable, which algebraically means that f(x) is continuous and f ' (x) is also continuous. This involves solving a simple system of equations. Passed out Q2 learning targets/grades list. "Crowdsourced" answers to selected problems on the chain rule handout hw. Used whiteboards to write problems that require particular differentiation rules to solve. Quickly reviewed the kinds of functions we know how to take derivatives of, and found that the 3 kinds still remaining are exponential, logarithmic, and inverse trigonometric. Here are their derivative rules:
Q2 standards/learning targets
Homework
- Copy down the above rules into your formula booklets
- On the chain rule handout from Wednesday, do: #11, 12 and #449, 450, 466
Resources
see wednesday's list