About This Chapter
Who's it for?
Anyone who needs help learning or mastering college calculus material will benefit from taking this course. There is no faster or easier way to learn college calculus. Among those who would benefit are:
- Students who have fallen behind in understanding derivatives or working with optimization and differentiation
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about the applications of derivatives
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Applications of Derivatives chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Applications of Derivatives chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any derivatives question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What does linearization mean, and how is it used to estimate the value of functions?
- What is Newton's Method, and how is it used to calculate the roots of equations?
- What are the five steps used in mathematical optimization?
- What do I do to optimize simple and complex systems?
1. Linearization of Functions
Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!
2. How to Estimate Function Values Using Linearization
Sometimes landing on Mars isn't that easy. You might need to use linearization to estimate if you will crash into the planet, or miss it entirely. Learn how to do just that in this lesson.
3. What is Newton's Method?
Hang gliding can be perilous, especially if you think you might land in a stinky pigpen. In this lesson, find out how Newton's Method might help you determine whether you'll be covered in mud when you land.
4. How to Use Newton's Method to Find Roots of Equations
Finding the roots of equations usually requires the use of a calculator. However, in this lesson you'll use Newton's Method to find the root of any equation, even when you can't solve for it explicitly.
5. Optimization and Differentiation
In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.
6. Optimizing Simple Systems
Optimization problems may seem overwhelming, but they can actually be quite simple. In this lesson, learn how to use a handy five-step formula to tackle these daunting problems.
7. Optimizing Complex Systems
In this lesson, you'll learn how to follow a five-step process to solve complex optimization problems by visualizing, defining, writing an equation, finding the minimum or maximum, and answering the question.
8. Finding the Second Derivative: Formula & Examples
In this lesson, you will learn the two-step process involved in finding the second derivative. Also, look at some examples to get your feet wet before jumping into the quiz.
9. First Derivative: Function & Examples
In this lesson, you will learn about the relationship between the first derivative and rates of change. You will learn how to find the derivative of a polynomial using limits.
10. Implicit Differentiation: Examples & Formula
This lesson will take you through the method of implicit differentiation with multiple examples and a quiz at the end to test your knowledge. Implicit differentiation utilizes all of your basic derivative rules to find the derivative of equations that are not in standard form.
11. Finding the Derivative of cot(x)
In this lesson we will find the derivative of cotangent by using trigonometric identities and the quotient rule.
12. Finding the Derivative of 2sinxcosx
Do you know how to take the derivative of a compound function? This lesson goes over a step-by-step process for using the product rule for taking the derivative of 2sin(x)cos(x).
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Other chapters within the Calculus: Help and Review course
- Graphing and Functions: Help and Review
- Continuity in Calculus: Help and Review
- Geometry and Trigonometry in Calculus: Help and Review
- Using Scientific Calculators in Calculus: Help and Review
- Limits in Calculus: Help and Review
- Rate of Change in Calculus: Help and Review
- Calculating Derivatives and Derivative Rules: Help and Review
- Graphing Derivatives and L'Hopital's Rule: Help and Review
- Area Under the Curve and Integrals: Help and Review
- Integration and Integration Techniques: Help and Review
- Integration Applications: Help and Review
- Differential Equations: Help and Review