## The Chain Rule

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

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

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

- Complete practice problem 2 on page 2
- Check solution to practice problem 2 on page 7

## Implicit Differentiation

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Implicit differentiation defined.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

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

- Complete exam problem 4 on page 1
- Check solution to exam problem 4 on page 1

Finding the derivative of an implicitly defined function.

- Complete exam problem 3 on page 1
- Check solution to exam problem 3 on page 1

## Example of Implicit Differentiation

Implicit differentiation demonstrated through an example.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

## Derivatives of Combinations of Functions

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.

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

## Continuously Compounded Interest

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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete practice problem 3 on page 2
- Check solution to practice problem 3 on pages 8–9

## Derivatives of Exponential and Trigonometric Functions

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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete practice problem 4 on page 2–3
- Check solution to practice problem 4 on pages 9–10

## Implicit Differentiation and Tangent Line to a Graph

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

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete exam problem 3 on page 4
- Check solution to exam problem 3 on pages 4–5

## Evaluating Derivatives

Two questions finding the derivatives of functions.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 1 to 2 on page 1
- Check solution to exam problems 1 to 2 on page 1

## Chain Rule and Implicit Differentiation

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

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 1F–1 to 1F–8 on page 5
- Check solution to exam problems 1F–1 to 1F–8 on pages 10–11