Section 1.5: Introduction to Derivatives
Key Concepts
Lessons for Section 1.5:
Derivatives
1. Introduction to Derivatives (an online lesson explaining what derivatives are)
2. Definition of Derivative
1. Introduction to Derivatives (an online lesson explaining what derivatives are)
2. Definition of Derivative
3. Definition of Derivative AGAIN! (To make sure you really get it!)
4. Applying Definition of Derivative (Example 1) **Always simplify your expression first before evaluation!**
5. Applying Definition of Derivatives (Example 2 - Simple Rational Function and Equation for the Tangent Line)
4. Applying Definition of Derivative (Example 1) **Always simplify your expression first before evaluation!**
5. Applying Definition of Derivatives (Example 2 - Simple Rational Function and Equation for the Tangent Line)
6. Derivative Notation (Let's learn the math language for derivatives!)
Note - Differentiation is the process of getting the derivative of a function. (Differentiate is the action word!)
Note - Differentiation is the process of getting the derivative of a function. (Differentiate is the action word!)
The First Principles
The Derivative from First Principles (a lesson with detailed examples on differentiation from First Principles)
The Derivative Function
1. What is a Derivative Function?
2. Derivative of a Linear Function (It's the slope!)
3. Applying Derivative of a Linear Function (Example 1)
4. Derivative of a Power Function
5. Applying Derivative of a Power Function (Example 1)
6. Finding the Equation of a Tangent Line at a Particular Point
7. Derivative of a Rational Function and Finding the Equation of a Tangent (Check eBook Examples 2 & 4)
8. Summary: The Derivative (More explanation on derivatives and step-by-step problem solving examples)
Expectations for this section:
- You must use the First Principles to find first the derivative function then the slope of a tangent to a curve.
- The Power Rule for finding the derivative of a power function will be covered in Unit 2.
- After Unit 2, you can use the Power Rule to find the slope of a tangent to the curve of a power function.
8. Summary: The Derivative (More explanation on derivatives and step-by-step problem solving examples)
Expectations for this section:
- You must use the First Principles to find first the derivative function then the slope of a tangent to a curve.
- The Power Rule for finding the derivative of a power function will be covered in Unit 2.
- After Unit 2, you can use the Power Rule to find the slope of a tangent to the curve of a power function.
Summary of Section 1.5:
Assigned Practices:
- eBook: Read p. 49 to 57
- eBook: Do exercises on p. 58 #1 to 13
- eBook: In-Class exercises p. 60 #14 to 16, #18 to 20