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Standard D05: Chain Rule + Advanced Techniques:
​Derivatives of Inverse Functions & Implicit Differentiation

Overview

D05 Standard Document

Objectives & Resources

1. Understand that the derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies, including knowledge of inverse function relationships and “implicit differentiation.” [EU 2.1]
2. Inverse Functions & Derivatives: Know that the chain rule can be used to find the derivative of an inverse function, provided the derivative of that function exists. [EK 2.1C6]
     a. Know and understand the equation that relates the derivatives of a function and its inverse (see below).

Use your knowledge of inverse function relationships!

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EXPLORATION
​   
Desmos: Derivatives of Inverse Functions
     b. Know the derivative rules for the inverse trigonometric functions.
     c. Know the derivative rule for the general logarithmic function.

Know these derivative rules. Flash cards might help!

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EXPLORATION Desmos: arcsine
EXPLORATION Desmos: arccosine
EXPLORATION Desmos: arctangent
EXPLORATION Desmos: general logarithmic function (base b)
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PRACTICE
     TEXTBOOK 3.6
  • Exercises 3, 5, 6, 22, 23, 24, 25, 28, 30.
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PRACTICE
​     
KHAN ACADEMY
  • Derivatives of Inverse Functions
  • Derivatives of Inverse Trigonometric Functions
  • Differentiate Logarithmic Functions​
3. Implicit Differentiation: Be able to calculate derivatives using implicit differentiation.
  • Know that the chain rule is the basis for implicit differentiation. [EK 2.1C5]
  • Know that the derivative rules we have learned tell us how to do EXPLICIT differentiation. We often use IMPLICIT differentiation in situations where explicit differentiation is difficult or impossible. We do not find an explicit formula for the derivative function, but we do find a way to evaluate derivative values at specific points.

We often use IMPLICIT differentiation in situations where EXPLICIT differentiation (using derivative rules) is difficult or impossible.

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PRACTICE
     TEXTBOOK 3.7
  • ​Exercises: 2, 3, 4, 9, 13, 15, *16, 23, 27, 31, 33.
  • Desmos graphs of the 3.7 Exercise functions
These graphs are unusual and FUN!
TEXTBOOK 3.7  EXERCISE 2
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PRACTICE
​     KHAN ACADEMY
  • Implicit Differentiation

SAMPLE CONTENT ASSESSMENT ITEMS

D05 Sample Assessment Questions & KEY
File Size: 267 kb
File Type: pdf
Download File

D05 "Pop Quiz"
File Size: 82 kb
File Type: pdf
Download File

D05 "Pop Quiz" KEY
File Size: 277 kb
File Type: pdf
Download File

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      • L01
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      • D01 old
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      • D06
      • D07
      • D08 >
        • Max Volume Sample
      • N01
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      • N07
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      • AP EXAM PREP
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      • P03
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