Introduced the product and quotient rules for differentiation and worked through several examples. Lecture notes here
Here is a proof of the product rule following the limit definition of derivative. Note that his final result differs from our version of the formula, but note that addition and multiplication are commutative operations. https://www.youtube.com/watch?v=L5ErlC0COxI
Quotient rule proof: https://www.youtube.com/watch?v=rKtkqMwtkR8
Homework: this worksheet #1-5 for Wednesday
Resources:
product rule example: https://www.youtube.com/watch?v=uPCjqfT0Ixg
quotient rule example: https://www.youtube.com/watch?v=PkdYCDA0CWU
(note that this example uses a slightly different formula than we do. also it explains that Snow White thing I mentioned kind of)
Warm up allowed us to use the quotient rule to find the derivative of tan(x). (Method here) Then wrote down it and the other trig derivatives into our foldable books. Went over the homework on the product and quotient rule. Then saw how to use a table to find derivatives involving the sum, difference, product, and quotient of functions. Learned about the chain rule, one of the most important rules in differential calculus. Saw some examples and wrote some formulas down. Here is the animation we looked at . Worked through a polynomial example as well as some trig examples, including using the chain rule twice. Finally looked at vertical tangents and differentiability and saw how a function is differentiable only when its derivative is continuous. Then passed out a practice assessment. PRACTICE SOLUTIONS HERE
Lecture Notes HERE
Homework:
p. 125: 16-18, 43-46, 70, 73, 74
p. 136: 8, 9, 24, 49, 56
(D-CD1 thru 6)
Resources:
simple chain rule examples: https://www.youtube.com/watch?v=6kScLENCXLg
chain rule using a table (!!!) https://www.youtube.com/watch?v=92iQu2AARL4
more chain rule examples: https://www.youtube.com/watch?v=6_lmiPDedsY
vertical tangent lines/differentiability: https://www.youtube.com/watch?v=E50E-kRyMPs
horizontal tangent lines: https://www.youtube.com/watch?v=4F1tKhehhbI
trig derivatives (with chain rule) https://www.youtube.com/watch?v=xJ3C_pZssJI
Went over homework on product, quotient, and chain rules. Discussed sample assessment. Took first assessment on derivatives. Handed out worksheet on trig derivatives and the derivative rules (product power quotient and chain).
Homework: (due Wednesday)
worksheet linked here selected problems:
2.8: 447*, 448, 455, 459, 464
2.9: 475-481, 482, 485*, 488*
(* problems with asterisk we will cover how to do on Monday, along with units/rates/higher order derivatives)
resources:
trig examples 1: https://www.youtube.com/watch?v=cZSbjtzfxNk
trig examples 2: https://www.youtube.com/watch?v=XoIe_t80PxM