## 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

3.

4. Applying Definition of Derivative (

5. Applying Definition of Derivatives (

**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)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!)**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.

8.

- 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.

**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.

**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