Differential calculus | Differential equations
In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. Differentiation with respect to time or one of the other variables requires application of the chain rule, since most problems involve several variables. Fundamentally, if a function is defined such that , then the derivative of the function can be taken with respect to another variable. We assume is a function of , i.e. . Then , so Written in Leibniz notation, this is: Thus, if it is known how changes with respect to , then we can determine how changes with respect to and vice versa. We can extend this application of the chain rule with the sum, difference, product and quotient rules of calculus, etc. For example, if then (Wikipedia).
Setting up related rates equation for word sums.
From playlist Differentiation
Ratios (Connecting Rates with Ratios and Simplifying to compare similar results)
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From playlist Working with Rates and Ratios
Calculus 1 Lecture 2.8: Related Rates
Calculus 1 Lecture 2.8: Related Rates
From playlist Calculus 1 (Full Length Videos)
Related Rates: Determine dy/dt Given a Function of x (Basic Example)
This video provided an introductory example of a related rates problem.
From playlist Related Rates
From playlist a. Numbers and Measurement
Calculus Lecture: Related Rates
This is a video lecture for the topic of related rates for Calculus I. In this video, I work through several examples and give an outline for how to approach these types of problems.
From playlist Calculus
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From playlist Calc 1
Applied Calculus – Section (3.6) – Related Rates This lecture discusses the basics for setting up a related rates problem. We identify the variables and the variables rates of change, then invoke a fundamental formula to link the related variables such as Pythagorean Theorem, area formulas
From playlist Applied Calculus
Math 030 Calculus I 040115: Related Rates Problems, ct'd.
Related rates problems: examples
From playlist Course 2: Calculus I
Math 2A. Calculus. Lecture 18. Related Rates.
UCI Math 2A: Single-Variable Calculus (Fall 2013) Lec 18. Single-Variable Calculus -- Related Rates -- View the complete course: http://ocw.uci.edu/courses/math_2a_calculus_i.html Instructor: German A. Enciso, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info
From playlist Math 2A: Calculus.
Calculus AB Lesson 4.2: Related Rates
================================= AP Calculus AB / IB Math SL Unit 4: Applications of the Derivative Lesson 2: Related Rates =================================
From playlist AP Calculus AB
Calculus AB Homework 4.2: Related Rates
Download Packet: https://goo.gl/tg9SDC ================================= AP Calculus AB / IB Math SL Unit 4: Applications of the Derivative Lesson 2: Related Rates =================================
From playlist AP Calculus AB
Worldwide Calculus: Related Rates
Lecture on 'Related Rates' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Related Rates Introduction Area & Volume 4K
I introduce Related Rate problems in Calculus and work through 2 examples Example 1 Radius related to area of a circle 3:54 Example 2 Volume of cone to changing height 17:08 Old Related Rates Lessons https://www.profrobbob.com/calculus/related-rates Check out http://www.ProfRobBob.com, th
From playlist Calculus (New)
Math 030 Calculus I 033015: Derivatives of inverse trigonometric function; Related Rates
Derivatives of inverse trigonometric functions; introduction to related rates problems
From playlist Course 2: Calculus I