---
# System prepended metadata

title: Daily Prep 4A -- MTH 201-04
tags: [' dailyprep', mth201]

---

---
tags: mth201, dailyprep
---

# Daily Prep 4A -- MTH 201-04

## Overview 

All three modules leading up to this point have focused on what a **derivative** is: Its origins in average velocity and rate of change, what it tells us about the function we are differentiating, and the information contained between a function and its first two derivatives. In Module 4 we shift focus to **computing derivatives** by introducing some shortcut methods that will replace taking limits and using the definition. In Module 4A we begin this process by looking at shortcut methods for elementary functions: constant, power, and exponential functions along with basic combinations of these. 

## 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. 

-  Compute (without using limits) the derivatives of constant, power, and exponential 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. 

-  Compute the derivative of constant multiples and sums of constant, power, and exponential functions.
- Use basic derivative rules to solve problems about slopes, velocities, and rates of change involving basic functions.


## Resources for learning

**Reading:** Read through [Section 2.1]([https://activecalculus.org/single/sec-2-1-elem-rules.html](https://activecalculus.org/single/sec-2-1-elem-rules.html)) of the *Active Calculus* textbook. Work through the examples and all interactive exercises found at the end of the section.

**Video:** At the MTH 201 playlist on YouTube (http://bit.ly/GVSUCalculus), watch the following videos. The total running time is 23:06.

- Screencast 2.1.1 -- Quick Review of elementary derivative rules (3:33) https://www.youtube.com/watch?v=wFOgWzI0SuQ
- Screencast 2.1.2 -- Derivatives of power and constant functions (5:19) https://www.youtube.com/watch?v=ciBNzth33Fw
- Screencast 2.1.3 -- Derivatives of exponential functions (2:54) https://www.youtube.com/watch?v=kcQieXhoAqs
- Screencast 2.1.4 -- Derivatives of constant multiples (4:06) https://www.youtube.com/watch?v=gya8IngB1BI
- Screencast 2.1.5 -- Derivatives of sums (7:14) https://www.youtube.com/watch?v=BaAj1IZvt-w


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.

**Other:** Desmos can't be used for the kinds of computation we're doing in this Module, but [Wolfram|Alpha](http://www.wolframalpha.com) excels with this. Just enter in "derivative of" and then the function you are given, and hit enter. Here's an example: https://www.wolframalpha.com/input/?i=derivative+of+3x%5E7+%2B+7x%5E3+%2B+1%2Fx  **Because technology is so good at doing the computations, doing the computations is not the main point of the Module or the course. It's about application and interpretation!** 

## Exercises 

The exercises for this Daily Prep are found on a Google Form this time, rather than a Desmos activity: 

https://docs.google.com/forms/d/e/1FAIpQLSft4_bD89ZZ9ASxeSXExSkP11OE1Ce0Rk87x8jIECUOtPWofg/viewform


## 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.