Calculus - Unit 7 - Definition and Basic Derivative Rules

Calculus - Unit 7 

Definition and Basic Derivative Rules

Defining average and instantaneous rates of change at a point

Notes:

Derivative notation review

Videos:
Newton, Leibniz, and Usain Bolt
Derivative as a concept
Secant lines and average rate of change
Derivative as slope of a curve
The derivative and tangent line equations


Assignments:
Secant lines and average rate of change
Derivative as slope of a curve
The derivative and tangent line equations

Defining the derivative of a function and using derivative notation

Notes:
Finding the tangent line equations using the formal definition of a limit

Videos:
Formal definition of the derivative as a limit
Formal and alternate form of the derivative
Example: Derivative as a limit
Example: Derivative from limit expression
Using the formal definition of the derivative
The derivative of x^2 at any point using the formal definition

Assignments:
Derivative as a limit

Estimating derivatives of a function at a point

Videos:
Estimating Derivatives

Assignments:
Estimating Derivatives

Connecting differentiability and continuity

Notes:
Differentiability implies continuity

Videos:
Differentiability and continuity
Differentiability at a point: Graphical
Differentiability at a point: Algebraic

Assignments:
Differentiability at a point: Graphical
Differentiability at a point: Algebraic

Applying the power rule

Videos:



Assignments:

Derivative rules: constant, sum, difference, and constant multiple introduction

Notes:

Videos:


Assignments:

Derivative rules: constant, sum, difference, and constant multiple: Connecting with the power rule

Notes:

Videos:

Assignments:

Derivatives of trigonometry and logarithms

Videos:


Assignments:

The Product Rule

Videos:


Assignments:

The quotient rule

Notes:

Videos:


Assignments:

Derivatives of inverse trigonometry functions

Notes:

Videos:


Assignments: