Chapter 3.6
Related rates
What You'll Learn
Identify two related quantities where one rate of change is easier to find than the other
Write equations relating quantities using geometry, volume formulas, or other relationships
Apply the Chain Rule to differentiate both sides of an equation with respect to time
Substitute known rates and values to solve for the unknown rate at a specific moment
Interpret negative rates as decreasing quantities and positive rates as increasing quantities
What You'll Practice
1
Solving ladder problems using the Pythagorean theorem and related rates
2
Finding rates of change for expanding spheres using volume formulas
3
Differentiating implicit equations with respect to time using the Chain Rule
4
Substituting given information into differential equations to solve for unknown rates
Why This Matters
Related rates are essential for solving real-world problems where multiple quantities change simultaneously, like inflating balloons, moving objects, or changing distances. This technique is fundamental in physics, engineering, and any field requiring dynamic analysis of connected systems.
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Chain Rule
Implicit Differentiation
Related Rates
Derivatives
Problem Solving
Geometry
Volume Formulas
