Week of November 30th
Tues, Dec. 2nd: Inverse Trig Functions, Review of 2.6, 2.7 & 2.8
Objectives
- Memorize the derivatives of the inverse sine, inverse cosine, and inverse tangent functions (you do not have to memorize the derivatives of cot, sec, and csc.
- Be able to compute the derivatives of all six inverse functions in problems.
Study Materials
- Watch video on Inverse Trig Functions:
- Work through the following problems as a review of the week before Thanksgiving:
- Chapter 2 Review #s 37 – 40 (Derivs of Exp and Log functions)
- Chapter 2 Review #s 13, 65, 66 (Implicit Differentiation)
- Click here for solutions.
Section 2.9: The Mean Value Theorem (Thurday)
Objectives
- Memorize Rolle’s Theorem and use in problems similar to Ex. 9.1.
- Use theorems 9.2 and 9.3 to determine the number of zeros in a function.
- Memorize the MVT and use in problems similar to Ex. 9.3.
- Understand Corollary 9.1 and use to solve problems similar to Ex. 9.4.
Study Materials
Video on Lesson 2.9
Week of November 23rd
Happy Thanksgiving!
Week of November 16th
2.6: Derivatives of Trig Functions (Tuesday)
Objectives
- Know the derivatives of the six trig functions.
- Use these derivatives in problems in conjunction with the product, quotient, and chain rules.
- Solve Application problems involving derivatives of trig functions
Study Materials
2.7: Derivatives of Exponential and Logarithmic Functions (Thursday)
Objectives
- Know the derivatives of ax, ex, logax, and lnx.
- Use these derivatives in problems in conjunction with the product, quotient, and chain rules.
Study Materials
Click here to download the powerpoint for Lesson 2.7.
2.8: Implicit Differentiation (Friday)
Objectives
- Understand what it means for a function to be defined implicitly.
- Solve problems using implicit differentiation.
Week of November 9th
We just reviewed and did examples this week. See the documents below.
Product rule proof and Chain Rule examples
Week of November 2nd
Click here to download a summary of all the rules learned this week!
2.3: The Power Rule
Objectives
- Know the power rule and use to find derivatives
- Know and apply theorem 3.3 (derivative of a sum, a difference, and a constant times a function)
- Find higher order derivatives (second, third derivatives, etc.)
2.4: The Product and Quotient Rules
Objectives
- Understand and be able to do the proof of the product rule
- Find derivatives of products
- Understand and be able to do the proof of the quotient rule
- Find derivatives of quotients
- Solve application problems
Study Materials: Proof of the Product Rule Video
2.5: The Chain Rule
Objectives
- Know the chain rule.
- Apply to various types of functions:
- Graphically Defined
- Numerically Defined
- Algebraically Defined
Week of Oct. 26th
2.2: The Derivative
Objectives
- Compute the derivative of a function using Defn. 2.2 (the definition of the derivative).
- Sketch a graph of f ‘(x) given a graph of f(x).
- Sketch a possible graph of f(x) given a graph of f ‘(x).
- Explain the relationship between the graph of a function and the graph of its derivative.
- Find points at which a function is not differentiable.
- by looking at the graph.
- by calculating the derivative algebraically (see Ex. 2.7)
- Approximate derivatives by looking at a table of values (numerically).
