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Chain Rule & Implicit Differentiation

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Lecture Notes

The Chain Rule (18.01, Fall 2005)

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Section 4, Page 3

Chain Rule for derivatives, including definition of composite functions and a worked example.

Prior Knowledge: Derivative as the Limit of a Difference Quotient (section 2 of lecture 1)
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Implicit Differentiation (18.01, Fall 2005)

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Section 5, Page 3

Implicit differentiation defined.

Prior Knowledge: None
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Example of Implicit Differentiation (18.01, Fall 2005)

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Section 1, Page 1

Implicit differentiation demonstrated through an example.

Prior Knowledge: Implicit Differentiation (section 5 of lecture 4) and Derivative of xn (section 3 of lecture 3)
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Online Textbook Chapter

Derivatives of Combinations of Functions (18.013A, Spring 2005)

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Rules for the derivatives of sums and products of functions, as well as the chain rule and rules for finding the derivative of an inverse function.

Prior Knowledge: Differentiability (OT6.1)
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Practice Problems

Chain Rule (18.01, Fall 2005)

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Problem 2 (page 2)

Two part question that involves applying and explaining the chain rule for derivatives.

Prior Knowledge: None

Solution (PDF) Page 7

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Continuously Compounded Interest (18.01, Fall 2005)

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Problem 3 (page 2)

Two part question involving a bank's liability from a loan and a savings account, each with continuously compounded interest.

Prior Knowledge: None

Solution (PDF) Pages 8 to 9

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Derivatives of Exponential and Trigonometric Functions (18.01, Fall 2005)

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Problem 4 (page 2 to page 3)

Taking the first and second derivatives of a function involving an exponential and a cosine.

Prior Knowledge: None

Solution (PDF) Pages 9 to 10

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Exam Questions

Implicit Differentiation and Tangent Line to a Graph (18.01, Fall 2005)

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Problem 3 (page 4)

Finding the equation of a tangent line to the graph of a function that is defined with an implicit equation.

Prior Knowledge: None

Solution (PDF) Pages 4 to 5

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Evaluating Derivatives (18.01, Fall 2006)

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Problem 1 (page 1) to problem 2 (page 1)

Two questions finding the derivatives of functions.

Prior Knowledge: None

Solution (PDF)# Page 1

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Implicit Differentiation (18.01, Fall 2006)

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Problem 4 (page 1)

Finding the derivative of the inverse sine function using implicit differentiation.

Prior Knowledge: None

Solution (PDF)# Page 1

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Implicit Differentiation (18.01, Fall 2006)

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Problem 3 (page 1)

Finding the derivative of an implicitly defined function.

Prior Knowledge: None

Solution (PDF)# Page 1

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Chain Rule and Implicit Differentiation (18.01, Fall 2006)

Document PDF - 2.2 MB
Problem 1F-1 (page 5) to problem 1F-8 (page 5)

Eight questions which involve finding derivatives using the Chain rule and the method of implicit differentiation.

Prior Knowledge: None

Solution (PDF - 4.0 MB) Pages 10 to 11

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