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

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

Implicit differentiation demonstrated through an example.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

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:**

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

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

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

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

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