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Jan 9, 2024
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Learning Guide Unit 5 -MATH 1211
Calculus (University of the People)
Studocu is not sponsored or endorsed by any college or university
Learning Guide Unit 5 -MATH 1211
Calculus (University of the People)
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MATH 1211-01 Calculus - AY2023-T3
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MATH 1211-01 - AY2023-T3
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Learning Guide Unit 5
Learning Guide Unit 5
Learning Guide Unit 5
Overview
Unit 5: Derivatives of Inverse Functions, Exponential and Logarithmic Functions
Topics:
Derivatives of Inverse functions
More on derivatives of Exponential and Logarithm Functions
Logarithmic Differentiation
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Learning Objectives:
By the end of this Unit, you will be able to:
1.
Calculate derivatives of inverse functions, particularly the inverse of trig functions.
2.
Calculate derivatives of exponential and logarithm functions 3.
Apply logarithmic differentiation to derivatives of complex functions.
Tasks:
Peer assess Unit 4 Written Assignment
Read the Learning Guide and Reading Assignments
Participate in the Discussion Assignment (post, comment, and rate peers’ submission in the Discussion Forum)
Complete and submit the Written Assignment
Make entries to the Learning Journal
Take the Self-Quiz
Introduction
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There are two major concepts we want you to learn and understand in this unit. One of them is how to find the derivative of an inverse function if you know the derivative of the original function. That is, given the function , if you know what is , how do you find . You must read the second paragraph of the textbook, page 302 to totally understand how this works. We find out that Downloaded by Whitney turner (ct8682126@gmail.com)
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The second concept applies to the function that looks like, . How do you find the derivative of this kind of function, for example, y=(x^2+3)^{sinx}? Make sure to relearn and remember the derivatives of exponential and logarithmic functions, the rules of the logarithm function, and then learn the concept of logarithmic differentiation. Read the Problem-
Solving strategy on page 331 and practice.
As you read through the material you should complete the problems listed for the Herman & Strang textbook in the Reading Assignment. You are strongly encouraged to memorize the derivatives of inverse trigonometric functions and the derivatives of the natural exponential and logarithmic functions.
Reading Assignment
Herman, E. & Strang, G. (2020). Calculus volume 1
. OpenStacks. Rice University.
Read Chapter 3, pages 302-308 and pages 322-333
o
sections 3.7, and 3.9
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Review the completed examples to understand the concepts and then complete some problems on your own. Review and practice will contribute to your success in this course.
You should attempt the problems in the book as indicated, and you are allowed to use the book and other resources to understand how to answer the problems. You are welcome to ask about these in the discussion forum.
o
3.7 #’s 265, 269, 275, 279, 281, 299, o
3.9 #’s 331,337,340,347,356, 361
The Organic Chemistry Tutor. (2016, September, 12)
. Derivatives of inverse functions [Video]. YouTube. https://youtu.be/Xq0YEXPwi4Y
This calculus video tutorial explains how to find the derivative of an inverse function. It contains plenty of examples and practice problems for you to master the concept. It shows you how to find the inverse function f^(-1) (x) from f(x) and how to calculate (f^(-
1) )^' (x) in terms of x and y. The Organic Chemistry Tutor. (2016, October 14). Logarithmic differentiation
[Video]
.
YouTube. https://youtu.be/9z1Dz60mWcQ
This calculus video tutorial explains how to perform logarithmic differentiation on natural logs and regular logarithmic functions including exponential functions such as e^x. It also provides the formulas and equations as well as the rules that you need to Downloaded by Whitney turner (ct8682126@gmail.com)
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apply use logarithmic differentiation to find the derivative of functions instead of using the product rule, quotient rule, or even the chain rule.
Discussion Assignment
In the discussion forum, you are expected to participate often and engage in deep levels of discourse. Please post your initial response by Sunday evening and continue to participate throughout the unit. You are required to post an initial response to the question/issue presented in the Forum and then respond to at least 3 of your classmates’ initial posts. You should also respond to anyone who has responded to you. Post an initial response in the discussion forum to the following:
Why might one prefer to use the logarithmic differentiation for finding derivatives of functions that have exponent?
Respond to your peers' posts and compare and contrast your ideas with theirs. Expand on their thoughts and ask c
needed. Your Discussion should be a minimum of 250 words in length and not more than 450 words. Please include a word count. Following the APA standard, use references and in-text citations for
the textbook and any other sources. Written Assignment
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1. Find the derivative for the function 2. Find the derivative for the function 3. Find the tangent line to at 4. Determine if is increasing or decreasing at the following points.
(a) z=1(b) z=5(c) z=20
5. Find the derivative for the function 6. Find the derivative for the function 7. Find the derivative for the function 8. Find for 9. Find for Learning Journal
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The Learning Journal is an evaluation tool designed to help you evaluate the importance of the material you learned but understand what you found relevant. In some cases, it should help you record problems you encountered but also how you resolved them. This does not mean you should resubmit what you already shared in the Discussions and assignments, but more relevant information. Learning Journals help you understand what information was presented and how you felt it interacted with your world.
Learning Journal prompt
Give one example of a mathematical idea from topics this week that you found creative and explain what you fin
example, you can choose an instance of creativity you experienced in your own problem-solving or something yo
person's definition or reasoning.
The Learning Journal entry should be a minimum of 400 words and not more than 750 words.
Self-Quiz
The Self-Quiz gives you an opportunity to self-assess your knowledge of what you have learned so far.
The results of the Self-Quiz do not count towards your final grade, but the quiz is an important part of the University’s learning process and it is expected that you will take it to ensure understanding of the materials presented. Reviewing and analyzing your results will help you perform better on future Graded Quizzes and the Final Exam.
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Please access the Self-Quiz on the main course homepage; it will be listed inside the Unit
.
Checklist
Peer assess Unit 4 Written Assignment
Read the Learning Guide and Reading Assignments
Participate in the Discussion Assignment (post, comment, and rate peers’ submission in the Discussion Forum)
Complete and submit the Written Assignment
Make entries to the Learning Journal
Take the Self-Quiz
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