Calculus
Chapter 4 - Calculating the Derivative
Section 4.1 - Techniques for Finding the Derivative
In this section we learn a much quicker way to find the derivative of a function.
This first video is the rules and some examples applying the rules to find the derivative.
The second video is applying the definition of a derivative using the quick method.
The third video talks about some common ideas for story problems.
Answers to Day 1 # 1-30
Answers to Day 2 # 31-45 (there is a error in question #44, the answer should be 42, f'(x) shouldn't have the +3 at the end.)
Answers to Story Problems 4.1
In this section we learn a much quicker way to find the derivative of a function.
This first video is the rules and some examples applying the rules to find the derivative.
The second video is applying the definition of a derivative using the quick method.
The third video talks about some common ideas for story problems.
Answers to Day 1 # 1-30
Answers to Day 2 # 31-45 (there is a error in question #44, the answer should be 42, f'(x) shouldn't have the +3 at the end.)
Answers to Story Problems 4.1
Section 4.2 - Derivatives of Products and Quotients
The first video of this section is the Product Rule with a basic example worked through.
This second video has a tougher example worked through dealing with the Product Rule.
This video gives a visualization of why the Product Rule is what it is. I found it helped explain the concept very well.
The second part of this section is the Quotient Rule. The first video is the formula and a basic example worked through.
This video is a tougher example using the Quotient Rule to find the derivative.
This video is a proof of the Quotient Rule. This is just if you are interested in where the formula comes from.
Answers to all of section 4.2
The first video of this section is the Product Rule with a basic example worked through.
This second video has a tougher example worked through dealing with the Product Rule.
This video gives a visualization of why the Product Rule is what it is. I found it helped explain the concept very well.
The second part of this section is the Quotient Rule. The first video is the formula and a basic example worked through.
This video is a tougher example using the Quotient Rule to find the derivative.
This video is a proof of the Quotient Rule. This is just if you are interested in where the formula comes from.
Answers to all of section 4.2
Calculus Review 4.1 - 4.2 Answers
Section 4.3 - Chain Rule
The Chain Rule is used to find the derivative of composite functions.
- Review of Composite Functions (4:32)
- The Chain Rule and some basic examples worked through. (5:26)
- A tougher example that needed to use the Product Rule with the Chain Rule. (5:41)
- Another tougher example that uses the Quotient Rule and the Chain Rule. (5:54)
Answers to section 4.3 *** there is an error on #26, it should be a "t cubed" ***
Answers to "Calculus Quiz Chain Rule Practice"
Answers to Story Problems
The Chain Rule is used to find the derivative of composite functions.
- Review of Composite Functions (4:32)
- The Chain Rule and some basic examples worked through. (5:26)
- A tougher example that needed to use the Product Rule with the Chain Rule. (5:41)
- Another tougher example that uses the Quotient Rule and the Chain Rule. (5:54)
Answers to section 4.3 *** there is an error on #26, it should be a "t cubed" ***
Answers to "Calculus Quiz Chain Rule Practice"
Answers to Story Problems
Section 4.4 - Derivatives of Exponential Functions
This is the notes with examples to finding the derivatives of exponential functions.
Answers to Section 4.4
Review Worksheet
This is the notes with examples to finding the derivatives of exponential functions.
Answers to Section 4.4
Review Worksheet
Section 4.5 - Derivatives of Logarithms
This video has the formulas for finding the derivatives of logarithmic functions, along with some examples.
Answers to Section 4.5
This video has the formulas for finding the derivatives of logarithmic functions, along with some examples.
Answers to Section 4.5