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Unit 3: Differentiation: Composite, Implicit & Inverse Functions

AP Calculus AB/BC

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3.0 Unit 3 Overview: Differentiation: Composite, Implicit, and Inverse Functions

Calculus AB: 9–13%

Implicit Derivatives

The derivative is the tool that is used to find the slope of a curve. We start by looking at the slope of a function which can be defined by the independent variable. In the case of a curve that is not explicitly defined by an independent variable we must use an implicit derivative, i.e. a derivative that will need to know the x value and the y value to compute the slope. This type of differentiation is a natural extension of the derivative of a function and we will show how to compute these implicit derivatives.

Practicing Derivative Rules II

In this session we will look at some practice problems that use the concept of calculating derivatives algebraically that were previously learned, using interaction with viewers. Rules focused on will include product and quotient rules, in addition to the chain rule as well as introducing some other one-step derivative rules

Practicing Derivative Rules II - Slides

Browse slides from the stream 'Practicing Derivative Rules II.'

Interpreting Derivatives through Graphs and in context - Slides

Browse slides from the stream 'Interpreting Derivatives through Graphs and in context.'

Interpreting Derivatives through Graphs and in context

This is a lesson on how to interpret derivatives through problems that may not involve algebraic manipulation of the derivative rules, but an understanding of them to be able to apply them to graphical data and within a context of a specific problem.

Interpreting Derivatives through Tables and in context - Slides

Browse slides from the stream 'Interpreting Derivatives through Tables and in context.'

Interpreting Derivatives through Tables and in context

We explore how to interpret derivatives (including using appropriate units and writing sentences to describe the meaning of a derivative in context), and look specifically at scenarios involving tables. We use average rate of change to estimate the derivative from a table of data, and finally use tables of data to define new functions and practice using the product, quotient, and chain rules.

The Chain Rule

In this session we will learn how to find the derivative of composite functions using the chain rule. Practice with different composite functions including but not limited to: polynomials and trigonometric functions. We will also practice combining the chain rule with product and quotient rules.

Helping Students Master Taking Derivatives Part II (for Teachers)

A look at how to get students comfortable with Implicit Derivatives and a way for students to understand (and not have to memorize) the Derivatives of Inverse Functions.

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3.1 The Chain Rule

🎥Watch: AP Calculus AB/BC - The Chain Rule

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3.2 Implicit Differentiation

🎥Watch: AP Calculus AB/BC - Implicit Derivatives

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3.3 Differentiating Inverse Functions

Inverse functions essentially “reverse” what the original function did. You likely encountered Inverse Functions in Algebra II and/or Pre-Calculus when reflecting a function along y = x.

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3.4 Differentiating Inverse Trigonometric Functions

Inverse Trigonometric Functions are - you guessed it - Inverse Functions with some added panache! They take Inverse Functions to the next level by adding in trigonometry.

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3.5 Selecting Procedures for Calculating Derivatives

🎥Watch: AP Calculus AB/BC - Practicing Derivative Rules II

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3.6 Calculating Higher-Order Derivatives

The term “higher-order derivative” may seem intimidating at first. However, this simply means that we can take the first derivative, second derivative, third derivative, and so on of a function.

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Free Review 2020

18 resources

Free Response Questions (FRQ)

10 resources

Unit 1: Limits & Continuity

24 resources

Unit 2: Differentiation: Definition & Fundamental Properties

19 resources

Unit 3: Differentiation: Composite, Implicit & Inverse Functions

16 resources

Unit 4: Contextual Applications of the Differentiation

11 resources

Unit 5: Analytical Applications of Differentiation

17 resources

Unit 6: Integration and Accumulation of Change

7 resources

Unit 7: Differential Equations

10 resources

Unit 8: Applications of Integration

16 resources

Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

11 resources

Unit 10: Infinite Sequences and Series (BC Only)

16 resources

Multiple Choice Questions (MCQ)

1 resource

Blogs

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