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Unit 2

2.0 Unit 2 Overview

2 min readโ€ขjuly 10, 2021


Unit 2 Overview

In this unit, you will learn more about derivatives, how they are defined, and the basic derivative rules (and exceptions). As one of the core foundations of analyzing functions and change in calculus itself, it is of utmost importance to gain an in-depth understanding of this unit before moving forward to more advanced concepts.๐Ÿ“‘ This unit makes up 10-12% of the Calculus AB exam and 4-7% of the Calculus BC exam.
This list will be a good place to start in terms of self-assessing ๐Ÿ“– what you need to study or learn.ย  As you are looking through this list write down what topics you donโ€™t remember or still need to learn.ย  You can then go to the full study guide page for each topic to get some more information!

Main Topics and Sections:

Instantaneous Rate of Change (2.1)

The rate of change at a particular point.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.07-eL4FUxV6tNZn.png?alt=media&token=3de0956c-832f-413d-ac39-a0ffc05b6153

Derivative Notation (2.2)

This notation is derived from the limit definition you learned in Unit 1. Rate of change at a particular point.
Think about the speed of something at a particular moment.ย  For example, if you were running a race, what is your speed at exactly 11 minutes?

Where Derivatives Exist (2.4)

There are 3 situations where a derivative doesnโ€™t exist.ย  These places are where there is a discontinuity, a corner/cusp, or a vertical tangent.
Corner/Cusp
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.09-zcjYj0t33p1T.png?alt=media&token=402f6a45-524c-487f-85ce-11d0681584fd
Vertical Tangent
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.10-RwadYjxV1kv7.png?alt=media&token=5594ec7d-4d8d-479c-b213-5c201cc67390
Discontinuity
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.10-Wi8pw75YBNNF.png?alt=media&token=f70fb508-d99c-48b5-8465-954969239f84

Power Rule (2.5)

For example, if you were taking the derivative of x^2, it would become 2x
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.13-AlT1b6HsFN7p.png?alt=media&token=2d304948-87af-4767-99f1-e7110da47787

Derivative Rule (2.6)

Sum Rule
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.15-0EpE1yWCco9P.png?alt=media&token=eab09968-4c2d-4e42-aae9-332ba91a893a
Difference Rule
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.26-gdkrYgJw7GWM.png?alt=media&token=bd7bf0c5-b3b8-45b6-b709-53d61cee705f
Constant Multiple Rule
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.26-qGB6RpPjhYR3.png?alt=media&token=369f5383-d33f-492f-8d49-5c4c642e54f8
Constant Rule
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.27-iiPs6lAuRD9L.png?alt=media&token=4e2c1096-6ecd-46bc-b4ec-5262288e11c0

Derivatives of Trig Functions (2.7 & 2.10)

You will need to memorize these! ๐Ÿง 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.28-o8v2vyI4UzAC.png?alt=media&token=8f563987-8461-4d31-aa2e-025ed617dcae

Product Rule (2.8)

Use this when taking the derivative of two functions that are multiplied together:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.30-jVaJCt6KQu5p.png?alt=media&token=e177cc32-55b1-46dc-a038-8f1312c27b03

Quotient Rule (2.9)

Use this when taking the derivative of two functions which are divided:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202021-06-14%20at%202.31-BuxOPkGsbqIS.png?alt=media&token=0f397f37-92ab-46df-96c0-80ccaee0b304

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