Warm up was to make a function differentiable. Reviewed a few homework problems on the chain rule, then reviewed exponential and log derivative problems through a few examples. Handed out exp and log properties handout.
Notes from board
HW answers for "The Rules" handout : link
Homework
choose any 6 from all 3 sections except 590-595: handout
due Thursday
Resources
some examples using log and exponent derivatives (made by me!) link
product and chain rule, combined with exp derivative (made by me!) first half of this
more examples link1 link2 link3 link4
Warm up was to take an exponential derivative involving the chain rule and evaluate it at a point. Second warm up was to write the equation of a line tangent to a function involving the product rule and an exponential derivative. Worked through 4 additional practice problems related to log and exp derivatives. Learned how to take the derivative of inverse sine, which opened up the last set of derivative rules to remember (the inverse trigs). The ones that start with 'c' are still negative, so you really only have to memorize sine, secant, and tangent.
Notes from board
Homework
choose any 6 from all 3 sections except 590-595: handout
due Thursday
Resources
an alternate way to find inverse sine derivative: link
see Monday above for log/exp help
Learned how to take derivatives involving product, quotient, power, and chain rules using a table.
Notes from board
Handout we did
Video example similar to DS: link
Warm up was to take and evaluate a derivative of an inverse trig function. Went over some homework (answers are below) and discussed an algebraic perspective on examining where functions are non-differentiable. This focused on first identifying whether or not they are continuous (which is a necessary but insufficient requirement) and then identifying whether the derivative is continuous as well. A function is not differentiable if either it or its derivative are not continuous. Also looked at how to take derivatives from a graph by using the chain rule. This allowed us to determine behavior of a function we could not actually see. Then passed out practice test.
Notes from board
"Excitement with Derivatives" hw answers here: LINK
Homework
work on the practice assessment (blank copy) (SOLUTIONS)
assessment is Monday
Resources
mixed derivative rules practice: LINK (D-AD2 and 2b)
product rule: LINK and Quotient Rule LINK D-AD3
chain rule examples: link (D-AD4)
product rule and chain rule combined; chain rule from a table LINK (D-AD4)
making a function differentiable (D-CD4): link
writing the equation of a tangent line (D-CD7): link