---
tags: mth201, dailyprep
---

# Daily Prep 6B -- MTH 201-04

## Overview

Module 6B introduces the last of our rules for differentiation. We'll apply the Chain Rule to find derivative formulas for **inverse functions** that are the "opposites" of other functions. Especially we will focus on the derivative of $y = \ln(x)$ and *inverse trigonometric functions* like $\arctan(x)$ and $\arcsin(x)$.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

+ *(Review)* Explain what is meant by an "inverse function" and the notation $f^{-1}$.
+ *(Review)* State the definitions of the functions $y = \log_b (x)$, $y = \ln(x)$, $y = \arctan(x)$, and $y = \arcsin(x)$ and important properties of these functions.
+ State the derivative of the function $y = \ln(x)$.
+ State the derivatives of the arcsine and arctangent functions.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

+ Find derivatives of inverse functions including logarithmic and inverse trig functions, in combination with other rules.

## Resources for learning

**Module 6B involves a significant amount of review of precalculus concepts, about logarithms and trigonometric functions.** If you don't have a strong background with this material, you may need to budget more time for review.

For this module you'll do a little reading from the prequel to MTH 201, a course we call **MTH 124, *Functions and Models***, in addition to reading from our text.

- First, read sections 1.7.1 and 1.7.3 from *Active Prelude to Calculus* (the text for MTH 124) and try the interactive exercise at the end: https://activecalculus.org/prelude/sec-changing-inverse.html
- After doing this, read sections 2.6.2 and 2.6.3 of *Active Calculus* and try the interactive exercises at the end: https://activecalculus.org/single/sec-2-6-inverse.html

**Video:** Watch the following from the GVSUMath Calculus playlist:

- Screencast 2.6.1: Quick review - Derivatives of inverse functions (3:25) https://www.youtube.com/watch?v=chdkxtt8XQo&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=46
- Screencast 2.6.2: Examples of derivatives with natural logarithm (6:30) https://www.youtube.com/watch?v=jhBhSerqbyU&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=47
- Screencast 2.6.3: Derivatives involving $\arcsin(x)$ https://www.youtube.com/watch?v=pEEQNdttZsw&list=PL9bIjQJDwfGuXQHuS5Jkmum_CFILoCZX-&index=48

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

The exercises for this Daily Prep are found on Desmos. Go to student.desmos.com and look for "MTH 201 Daily Prep 6B".

## Submission and grading

To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.)

A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.