Calculus

# Differentiation: definition and basic derivative rules

- Defining average and instantaneous rates of change at a point
- Defining the derivative of a function and using derivative notation
- Estimating derivatives of a function at a point
- Connecting differentiability and continuity: determining when derivatives do and do not exist
- Applying the power rule
- Derivative rules: constant, sum, difference, and constant multiple: introduction
- Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule
- Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)
- The product rule
- The quotient rule
- Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

Register for a session to review this topic with a small group of learners.

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

We will go over 1.6 - The Derivative as a Function

BL

JS

Jason S

0

10/20

Dr

Calculus · session

#### Basic Derivative Rules, chain rule, and trig functions!

We will review basic derivative rules before diving into some more complex composite functions' derivatives using chain rule, before introducing common trig derivatives. Open to any related questions and topics as well!

VK

Vedant K

2

1/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

- Average vs. instantaneous rates of change

- Limit definition of a derivative

- Differentiability criteria for a function

- Common derivatives to memorize

- Derivative rules for addition/subtraction

- Power rule

- Product rule

- Quotient rule

- Mean value theorem/Rolle's Theorem

SL

PM

Piyush M

0

9/15

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

We will be covering the following:

-Derivation of composite functions

-multiplication and division rules

RG

Rodas G

0

5/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Topics:

- Chain Rule with table

- Derivative of $a^x$

- Derivative of $7^{x^2-x}$

BL

WH

WASAY H

0

2/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

We will start learning about one of the most important topics in all of Calculus. Derivatives!

VS

Vikram S

0

0/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Topics:

- Introduction to implicit differentiation

- Worked examples

- Derivatives of inverse functions

_ Derivatives of inverse functions: Tables

BL

WH

WASAY H

0

2/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Unit II - The Derivative

-Intuitive introduction to the derivative

- Definition of the derivative

PL

JG

Jose Roberto Cossich G

0

2 spots left!

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

-Basic derivative laws

-The Chain Rule

PL

JG

Jose Roberto Cossich G

0

2 spots left!

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Topics:

- Derivative of inverse sin

- Derivative of inverse cosine

- Derivative of inverse tangent

BL

WH

WASAY H

0

2/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

-Rolle's Theorem and the Mean Value Theorem

-Implicit Differentiation

PL

JG

Jose Roberto Cossich G

0

2 spots left!

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

2.1 - What’s the limit definition of a derivative?

2.2 - How do we solve the limit form of a derivative?

2.3 - How can we estimate derivatives?

2.4 - What’s the definition of differentiability?

2.5 - What’s the power rule?

2.6 - How do we differentiate a function with multiple components?

2.7 - What are the derivatives for sin(x), cos(x), ex, and ln(x)?

2.8 - What is the product rule?

2.9 - What is the quotient rule?

2.10 - What are the derivatives of all trig functions?

BL

WB

William B

0

10/50

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Topics:

- Selecting strategies in finding derivatives

- Differentiation: finding error

BL

WH

WASAY H

0

2/20

Dr

Calculus · series session

#### Differentiation: definition and basic derivative rules

Topics:

- Second derivatives

- Second derivatives (implicit equations)

- Connecting derivatives with limits

BL

WH

WASAY H

0

2/20

### That's it for now!

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