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Rates of Change & Related Rates

Emily Davis

Emily Davis

6 min read

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Study Guide Overview

This study guide covers related rates problems, focusing on how to find rates of change using the chain rule and implicit differentiation. Key steps include forming equations that link rates, identifying known and unknown rates, and substituting values to solve. The guide also addresses additional considerations, such as multiple terms and variable types. Practice questions and a glossary are included for further understanding.

Solving Related Rates Problems

Table of Contents

  1. Introduction to Related Rates
  2. Steps to Solve Related Rates Problems
  3. Forming Equations for Related Rates
  4. Using Implicit Differentiation
  5. Additional Considerations
  6. Practice Questions
  7. Glossary
  8. Summary and Key Takeaways
Key Concept

Related rates problems involve finding the rate at which one quantity changes with respect to time, given the rate at which another quantity changes with respect to time.

  • Chain Rule: The fundamental tool for solving related rates problems. dydx=dydu×dudx\frac{dy}{dx}=\frac{dy}{du} \times \frac{du}{dx}
**Example**: If the volume VV of a balloon changes over time tt, and the radius rr of the balloon also changes over time, the chain rule helps relate dVdt\frac{dV}{dt} and drdt\frac{dr}{dt}.

  1. Form an equation linking the rates:

    • Identify the rate you are trying to find.
    • Determine the rates you know.
    • Identify any rates you can calculate through differentiation.

  2. Substitute known values to find the desired rate.

  1. **Identify the rate you are trying to...
Previous Topic - Motion in a Straight LineNext Topic - Approximating Values of a Function

Question 1 of 10

If dydu=3\frac{dy}{du} = 3 and dudx=2\frac{du}{dx} = 2, what is the value of dydx\frac{dy}{dx}?

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1.5

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