Standard D03: Finding Basic Derivatives
(focusing on analytical "symbolic" methods)
| d03rev20181101.pdf |
| d03rev20181101.docx |
Class Notes on Basic Derivative Rules:
| class_notes_basic_derivative_rules.pdf |
Desmos Activity:
This Desmos activity enables you to experiment in order to validate derivative rules for specific functions of your choice.
Objectives & Resources:
1. Understand that the derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies. [EU 2.1]
This Desmos activity enables you to experiment in order to validate derivative rules for specific functions of your choice.
Objectives & Resources:
1. Understand that the derivative of a function is defined as the limit of a difference quotient and can be determined using a variety of strategies. [EU 2.1]
- Khan video: Formal definition of the derivative as a limit
- Khan video: Formal and alternate form of the derivative
- a. Using the Definition: Know that direct application of the definition of the derivative can be used to find the derivative for selected functions, including polynomial, power, sine, cosine, exponential, and logarithmic functions. [EK 2.1C1]
- Khan video: The derivative of x² at x=3 using the formal definition
- Khan video: The derivative of x² at any point using the formal definition
- Khan practice: Derivative as a limit
- b. Using Derivative Rules: Know that specific rules can be used to calculate derivatives for classes of functions, including polynomial, rational, power, exponential, logarithmic, trigonometric, and inverse trigonometric. [EK 2.1C2] Know that sums, differences, products, and quotients of functions can be differentiated using derivative rules. [EK 2.1C3]
- Desmos Activity: This Desmos activity enables you to experiment in order to validate derivative rules for specific functions of your choice.
- Derivative of Constant Functions (Textbook 2.3, page 103)
- Khan video: Basic Derivative Rules (Part 1)
- Derivative of Linear Functions (Textbook 2.3, page 103)
- “Power Rule” (3.1, page 131) & Derivative of Power Functions (Textbook 2.3, page 103)
- Khan video: Power Rule
- Khan practice: Differentiate integer powers
- Khan practice: Power Rule (with rewriting expressions)
- Derivative of a Constant Multiple of a Function (Textbook 3.1, page 130)
- Khan video: Basic Derivative Rules (Part 2)
- Derivative of a Sum or Difference of Two Functions (Textbook 3.1, page 130)
- Khan video: Basic Derivative Rules (Part 2)
- Khan practice: Basic Derivative Rules: Find the error.
- Khan practice: Basic Derivative Rules: Table
- Khan review: Basic Differentiation Review
- Derivative of Polynomial Functions (3.1, page 134)
- Khan video: Differentiating Polynomials
- Khan practice: Differentiate Polynomials
- Khan practice: Tangent Lines for Polynomials
- Sample Assessment Questions: Textbook 3.1 (pages 136-139): 1, 3, 5, 7, 9, 11, 15, 17, 21, 23, 25, 29, 31, 35, 39, 43, 45, 57, 59, 63, 67, 69, 74, 85. (See Solution KEY on Husky Hub under TOPICS.)
- Derivative of Exponential Functions (3.2, pages 140 and 142)
- Khan video: Derivative of (natural) exponential function (e^x)
- Derivative of General Exponential Function (a^x) - see textbook, page 142
- Sample Assessment Questions: Textbook 3.2 (pages 143-144): 1-27 (odd), 41, 47. (See Solution KEY on Husky Hub under TOPICS.)
- Derivative of Logarithmic Functions (3.6, page 165)
- Khan video: Derivative of (natural) logarithmic function (ln x)
- Khan practice: Derivative of e^x and ln x
- Sample Assessment Questions: Textbook 3.6 (pages 167-168): 4, 37. (See Solution KEY on Husky Hub under TOPICS.)
- Derivative of Trigonometric Functions (3.5, pages 158-161)
- Khan video: Derivatives of sine and cosine functions
- Khan practice: Derivatives of sine and cosine
- Sample Assessment Questions: Textbook 3.5 (pages 162): 2. (See Solution KEY on Husky Hub under TOPICS.)
- “Product Rule” (3.3, page 145)
- Khan video: Product rule for derivatives
- Khan practice: Differentiate products
- Khan practice: Product rule with tables
- Sample Assessment Questions: Textbook 3.5 (page 162): 3, 12, 34, 35, 37, 48, 51. (See Solution KEY on Husky Hub under TOPICS.)
- Sample Assessment Questions: Textbook 3.6 (pages 167-168): 14, 16, 38. (See Solution KEY on Husky Hub under TOPICS.)
- “Quotient Rule” (3.3, page 146)
- Khan review: Quotient Rule
- Khan video: Quotient rule
- Khan practice: Differentiate quotients
- Khan practice: Quotient rule with tables
- Khan practice: Differentiate rational functions
- Sample Assessment Questions: Textbook 3.5 (page 162): 41, 42, 44. (See Solution KEY on Husky Hub under TOPICS.)
- Sample Assessment Questions: Textbook 3.6 (page 168): 33. (See Solution KEY on Husky Hub under TOPICS.)
- Derivative of Constant Functions (Textbook 2.3, page 103)