Syllabus for Math 181 - Calculus 1 at Nevada State College - Dr. Serge Ballif
The goal of this section is to develop derivative rules for the functions $y = \ln(x)$, $y = \arcsin(x)$, and $y = \arctan(x)$. These are very important functions in their own rights, and they are all defined as inverses of existing functions. The fact that they are inverse functions provides a one-size-fits-all method for determining their derivatives. We will briefly review the basic precalculus concepts about inverse functions and then see how the definition of an inverse function – in addition to the Chain Rule – leads to these three derivative rules as well as a general rule for differentiating any inverse function.
Basic objectives: Each student is responsible for gaining proficiency with each of these tasks prior to engaging in class discussions, through the use of the learning resources (below) and through the working of exercises (also below).
Advanced objectives: The following objectives are the subject of class discussion and further work; they should be mastered by each student during and following class discussions.
To gain proficiency in the learning objectives, use the following resources. You may include other resources if you wish, in addition to or in replacement of the following.
Textbook: In Active Calculus, read Section 2.6. Make sure to read actively, working through examples and activities as you go.
Video: There are two sets of videos to watch this time. The first set is review about inverse functions from precalculus mathematics, and runs a total time of about 35 minutes. I would recommend at least reviewing these videos for all students, and students who need a refresher course on inverse functions should give full attention to all of them. The second set is the core calculus material for this section, and each student should watch all of the videos (running time 14:24).
The following activity is to be done during and following your reading and viewing of the resources. Go to student.desmos.com and join using your name in the format Last, First. For example, I would enter my name as Ballif, Serge. Complete each part of the activity. Some of these problems will require you to work them out on paper before entering your answer. Practice producing high quality work so that your work is readable and meaningful. You will receive a mark of Pass if each item response shows a good-faith effort to be right and is submitted prior to the deadline. Remember to use the Piazza discussion board to ask about any questions you have.