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AP Calculus AB/BC

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Integration and Accumulation of Change

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The Fundamental Theorem of Calculus and Definite Integrals

Super Cool Worksheet: Advanced Chain Rule and More!

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Super Cool Worksheet: Advanced Chain Rule and More!
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emily_hyhf

@emily_hyhf

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Subject Expert

This advanced chain rule worksheet calculus and differentiation guide covers essential calculus concepts including chain rule, implicit differentiation, and inverse functions.

  • The chain rule, also known as the onion rule, is used for finding derivatives of composite functions
  • Implicit differentiation step-by-step guide explains how to differentiate equations where y is not isolated
  • The guide covers inverse function differentiation including mastering inverse trigonometric derivatives
  • Higher-order derivatives and special differentiation rules are explained systematically
  • Important domains and ranges for inverse trigonometric functions are clearly outlined

11/7/2023

172

CALC CHAPTER 3 CHEAT SHEET 3.1) The Chain Rule (Onion Rule) Nderivative of a composite function x f(g(x)) = f'(g(x))• g'(x) Alnx³ = 3nx dx 3

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Page 2: Advanced Differentiation Techniques

The second page delves into inverse trigonometric functions, domains of inverse functions, and higher-order derivatives. It provides comprehensive coverage of specialized differentiation procedures.

Definition: The derivative of arcsin(x) equals 1/√(1-x²), valid within the domain [-1,1].

Highlight: Higher-order derivatives are denoted as f'(x), f''(x), f'''(x), and f⁽ⁿ⁾(x) for the nth derivative.

Example: For inverse trigonometric functions, arctan(x) has a domain of all real numbers and range of (-π/2, π/2).

Vocabulary: The notation dy/dx represents the first derivative, while d²y/dx² represents the second derivative.

CALC CHAPTER 3 CHEAT SHEET 3.1) The Chain Rule (Onion Rule) Nderivative of a composite function x f(g(x)) = f'(g(x))• g'(x) Alnx³ = 3nx dx 3

View

Page 1: Core Differentiation Concepts

The first page introduces fundamental calculus concepts focusing on the chain rule, implicit differentiation, and inverse functions. The content systematically presents differentiation techniques essential for advanced calculus problems.

Definition: The chain rule states that the derivative of a composite function f(g(x)) equals f'(g(x)) multiplied by g'(x).

Example: When differentiating ln(x³), using the chain rule gives us 3/x.

Highlight: For implicit differentiation, remember to include dy/dx whenever differentiating terms containing y.

Vocabulary: Horizontal tangent lines occur when dy/dx = 0, while vertical tangent lines exist when dy/dx is undefined.

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Knowunity is the # 1 ranked education app in five European countries

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Subjects

/

AP Calculus AB/BC

/

Integration and Accumulation of Change

/

The Fundamental Theorem of Calculus and Definite Integrals

Super Cool Worksheet: Advanced Chain Rule and More!

user profile picture

emily_hyhf

@emily_hyhf

·

8 Followers

Follow

Subject Expert

This advanced chain rule worksheet calculus and differentiation guide covers essential calculus concepts including chain rule, implicit differentiation, and inverse functions.

  • The chain rule, also known as the onion rule, is used for finding derivatives of composite functions
  • Implicit differentiation step-by-step guide explains how to differentiate equations where y is not isolated
  • The guide covers inverse function differentiation including mastering inverse trigonometric derivatives
  • Higher-order derivatives and special differentiation rules are explained systematically
  • Important domains and ranges for inverse trigonometric functions are clearly outlined

11/7/2023

172

 

11th/12th

 

AP Calculus AB/BC

8

CALC CHAPTER 3 CHEAT SHEET 3.1) The Chain Rule (Onion Rule) Nderivative of a composite function x f(g(x)) = f'(g(x))• g'(x) Alnx³ = 3nx dx 3

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Page 2: Advanced Differentiation Techniques

The second page delves into inverse trigonometric functions, domains of inverse functions, and higher-order derivatives. It provides comprehensive coverage of specialized differentiation procedures.

Definition: The derivative of arcsin(x) equals 1/√(1-x²), valid within the domain [-1,1].

Highlight: Higher-order derivatives are denoted as f'(x), f''(x), f'''(x), and f⁽ⁿ⁾(x) for the nth derivative.

Example: For inverse trigonometric functions, arctan(x) has a domain of all real numbers and range of (-π/2, π/2).

Vocabulary: The notation dy/dx represents the first derivative, while d²y/dx² represents the second derivative.

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CALC CHAPTER 3 CHEAT SHEET 3.1) The Chain Rule (Onion Rule) Nderivative of a composite function x f(g(x)) = f'(g(x))• g'(x) Alnx³ = 3nx dx 3

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Core Differentiation Concepts

The first page introduces fundamental calculus concepts focusing on the chain rule, implicit differentiation, and inverse functions. The content systematically presents differentiation techniques essential for advanced calculus problems.

Definition: The chain rule states that the derivative of a composite function f(g(x)) equals f'(g(x)) multiplied by g'(x).

Example: When differentiating ln(x³), using the chain rule gives us 3/x.

Highlight: For implicit differentiation, remember to include dy/dx whenever differentiating terms containing y.

Vocabulary: Horizontal tangent lines occur when dy/dx = 0, while vertical tangent lines exist when dy/dx is undefined.

Sign up for free!

Learn faster and better with thousand of available study notes

App

By signing up you accept Terms of Service and Privacy Policy

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying