# Rules: Derivative of Sums, Products & Quotients of Functions

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## Lecture Notes

#### Linearity

PDF
Section 3, Page 3

Linearity of the derivative (derivative of sums of functions).

Instructor: Prof. Jason Starr
Prior Knowledge: Concept of Derivative (section 2 of lecture 1)

#### The Liebniz Rule / Product Rule

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Section 4, Page 3

Product rule for derivatives. Gives proof sketch.

Instructor: Prof. Jason Starr
Prior Knowledge: Concept of Derivative (section 2 of lecture 1)

#### The Quotient Rule

PDF
Section 5, Page 3 to page 4

Quotient rule for derivatives, derived using product rule.

Instructor: Prof. Jason Starr
Prior Knowledge: Product Rule (section 4 of this lecture) and Concept of Derivative (section 2 of lecture 1)

#### Product Rule Example

PDF
Section 1, Page 1

Product rule used to find a derivative.

Instructor: Prof. Jason Starr
Prior Knowledge: Product Rule (section 4 of lecture 3) and derivative of xn (sections 3 and 6 of lecture 3)

#### Logarithmic Differentiation

PDF
Section 5, Page 4 to page 5

Finding the derivative of a product of functions using logarithms to convert into a sum of functions. Includes worked example.

Instructor: Prof. Jason Starr
Prior Knowledge: Rules for Logarithms (section 2 of this lecture) and Product Rule (section 4 of lecture 3)

#### Differentials

PDF
Section 1, Page 1 to page 2

Differential notation for derivatives is explained and common rules for derivatives are listed in differential notation. Includes an example of a derivative taken in differential notation.

Instructor: Prof. Jason Starr
Prior Knowledge: Concept of Derivative (section 2 of lecture 1)

## Online Textbook Chapter

#### Derivatives of Combinations of Functions

Document

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.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Differentiability (OT6.1)

## Practice Problem

#### Derivatives of Exponential and Trigonometric Functions

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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.

Instructor: Prof. Jason Starr
Prior Knowledge: None

## Exam Questions

#### Evaluating Derivatives and Limits

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Problem 1 (page 1)

Four-part question involving the evaluation of three derivatives and a limit.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Evaluating Derivatives

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

Two questions finding the derivatives of functions.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Evaluating Derivatives

PDF
Problem 2 (page 1)

Finding the derivatives of four functions.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Evaluating Derivatives

PDF
Problem 1 (page 1)

Three derivatives to be evaluated using a variety of techniques.

Instructor: Prof. David Jerison
Prior Knowledge: None