How to Solve Related Rates Problems in 5 Steps :: Calculus

What are Related Rates problems and how are they solved?
In this video I discuss the application of calculus known as related rates. This video describes the properties of a related rates problem, how to solve a related rates problem in 5 steps, and how those steps are applied in an example word problem.
Video table of contents:
0:00 Introduction
0:32 What are Related Rates problems?
1:18 5 Steps to Solve Related Rates Problems
3:16 Related Rates: An Example Problem
3:56 Draw a diagram
5:05 Label all quantities and their rates of change
8:44 Relate all quantities in the same equation
9:33 Differentiate the equation with respect to time
10:42 Use the resulting equation to answer
If you have any questions, feel free to ask in the comments section.

[@fcar851]

Best lesson I've ever seen on Related Rates. Very very helpful the way Mr T set-up and solved this Rocket problem . Great teachers are hard to find . He is surely one !

[@abc-ex2ls]

This is the best explaination on related rates,hope theres more video from mr S Math

[@HanOnkel]

From the integral of my bottomless heart, thank you, Sir.

[@MrSMath]

You're very welcome!

[@jimmylavan26]

This is explained so well. I'd love to see you cover some conical tank and shadow problems using related rates.

[@jonasschmidt1119]

This really saved me! Cannot tell you how thankful I am for this video. Fantastic explanation. Wish me luck on my test tomorrow!

[@jwhebegw5401]

How it go

[@nextdoortutor]

Simple explanation. Love it! Awesome video!

[@LeNguyen-im8dm]

WOW. There are so many ways to solve and show the work. This way is the best and very organized. Thank you for the video.

[@MrSMath]

You are very welcome!

[@girishghadge8460]

Mr. Smith you made it so easy to understand thank you so much may god bless you Thanks again !!

[@MrSMath]

You are very welcome! Glad it helped!

[@renewd]

Nice clear method and explanation. Thank you, Mr. S!

[@MrSMath]

Glad it was helpful!

[@efiorentino1024]

very helpful. thanks

[@madalenegoeller6109]

Thank you so much! I actually feel like I understand the concept now!

[@sherwinjerome8518]

May you forever be granted the best gifts. Thank yo so much!!!!!

[@MrSMath]

You are welcome!!

[@GrowingRevolution]

very well done

[@sret5354]

W mans, underrated bro

[@brysonmutinda5280]

Great video sir.You really broke down the concept for easy understanding.

[@MrSMath]

Glad it was helpful!

[@themadladprince430]

Thank you

[@queenbreerobinson4354]

Can you PLEASE DO A VIDEO ON introduction to related rates with TWO EQUATIONS!? In calculus

[@errebusaether]

That was really fun to do.

[@dennisdemarcus720]

life saver

[@user-wp3io4rp5y]

good idea

[@gregzip4787]

i was kind of feeliing stressed about my test later this week but after this video i think im gonna do great.

[@MrSMath]

Good luck on the test - hope this helped

[@sadminer1339]

Thank you so much for this video you single handedly saved me from failing my calc test tmrw.

[@MrSMath]

You’re welcome - good luck on the test!

[@sadminer1339]

@@MrSMath Thanks I'm taking it in 1 hr

[@jacklandrey8847]

thank you!

[@MrSMath]

You're welcome!

[@ajayj2133]

Thanks ❤

[@MrSMath]

Welcome!

[@niche9015]

9:50 this is the part that still confuses me. Why do you differentiate and multiply each term?

[@PaulJackson157]

W in the chat thx man

[@MrSMath]

yw - glad it helped

[@bobjoe2538]

I have a clarifying question at 8:00, how did you simplify the a^2 and b^2 to get 5000 root 5??

[@MrSMath]

This was the Pythagorean Theorem. a^2+b^2=c^2. From the given information I knew that a=5000 and b=10000. To solve the Pythagorean Theorem for c I took the square root of both sides of the equation. Here, the square root of a^2+b^2 is the square root of 5000^2+10000^2, which simplifies to 5000 root 5.

[@bobjoe2538]

@@MrSMath Yea I know that part but I’m talking about the last part. How does it simplify to 5,000^5?

[@MrSMath]

Great question! That last part is a bit tricky because the numbers are so large. To simplify 5000^2+10000^2, first realize that 5,000 squared is 25 million and 10,000 squared is 100 million. Adding these gives a sum of 125 million. This is equal to c^2, so to find c you take the square root of 125 million. Simplifying the square root of 125 million is difficult because it is so large. Since 125 million is equal to 1 million times 125, I began by rewriting the square root of 125 million as the square root of 1 million times the square root of 125. The square root of 1 million is 1000, so it becomes 1000 root 125. Then, I rewrote the square root of 125 as the square root of 25 times the square root of 5. The square root of 25 is exactly 5, so now I have 1000 times 5 times the square root of 5. Multiplying 1000 and 5 gave me the final simplification which is 5000 root 5.

[@errebusaether]

@@bobjoe2538 Thank god, someone questioned this. Cause I had no literal idea how to solve this part. T-T

[@carpiojirohreinier2035]

How do you do Step 4 on V = πr^2h

[@MrSMath]

In that situation, the Product Rule is required when differentiating the right side of the equation. The result would be V' = π (r^2*h'+2rh*r')

[@fcar851]

Refering to Mr S math ..not Mr t

[@Kamotegsg]

7:45 i just need a clarification im hella confused

[@MrSMath]

The given information describes a situation that can be represented as a right triangle. Only two sides of the triangle are given in the problem. At 7:45 I used the Pythagorean Theorem to find the length of the third side. This theorem is a^2+b^2=c^2 where a and b are the legs of a right triangle and c is the hypotenuse. We are told what side a and side b are in the problem, at 7:45 I used this theorem to find side c.

[@Kamotegsg]

@@MrSMath no not that gow do you get the 5000 sqrt5?

[@Kamotegsg]

@@MrSMath and also whrre did you pull out the 5 bruhh

[@MrSMath]

In the video, I explain that side c is the square root of 5000 squared plus 10,000 squared. 5000^2 + 10000^2 is 125,000,000. The square root of 125 million simplifies to 5000 sqrt 5. I think the easiest way to simplify this is to find the square root of 1,000,000 (which is 1,000) times the square root of 125 (which is 5 sqrt 5). Then multiply these to get 5000 sqrt 5.