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Preview
Here's the on-ramp for this lesson.
What Will We Learn?
In this lesson we'll finish learning about differentiation rules by studying the Chain Rule (derivative rule for a composition of functions) and the Quotient Rule. Then, we'll wrap up the chapter by learning about the second derivative -- the derivative of the derivative function.
Why Do We Need to Learn This?
In addition to completing our study of the faster ways to calculate derivatives, this lesson introduces the notion of a second derivative. Intuitively, this new object measures the change of the change of the function. That may sound confusing, but you no doubt have intimate experience with second derivatives. For example, the feeling of being pushed back into your chair when the car you're in accelerates -- that's you feeling a second derivative (acceleration, the change in the velocity, itself the change in position). And as we'll learn later in Lesson 16, the second derivative f''(x) contains similar insights to the "first" derivative (what we'll henceforth call f'(x)). In particular, we'll learn then that f''(x) tells us about the curvature of the underlying function.
Review
Review
Learn
Learn
The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
Lesson Notes
Lesson Notes
Lesson 11.pdfVideo 1 (Examples 3.26-3.27)
Video 1 (Examples 3.26-3.27)
Video 2 (Examples 3.29-3.30)
Video 2 (Examples 3.29-3.30)
Video 3 (Examples 3.42-3.43)
Video 3 (Examples 3.42-3.43)
Reflect
Reflect
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Practice
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 11 PP.pdfPage updated
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