🪜 Related Rates: Ladder Sliding Down a Wall – Finding the Rate of Change of Area 🪜

Related Rates: Ladder Sliding Down a Wall – Finding the Rate of Change of Area

🪜 Explore Related Rates with the Ladder Sliding Down a Wall Problem! 🪜

In this calculus video, we tackle the classic related rates problem of a ladder sliding down a wall. As the ladder is pulled away from the wall, it slides downward, and our goal is to find the rate of change of the area underneath the ladder.

What You’ll Learn:

Understanding Related Rates: Get familiar with the principles of related rates through this practical example.

Step-by-Step Solution: Follow along as we break down the process:

Visualizing the Scenario: Create a diagram to illustrate the ladder's position and the area beneath it.

Identifying Variables: Determine the relevant dimensions and rates of change involved in the problem.

Setting Up the Equation: Establish the relationship between the ladder's length, the height on the wall, and the area underneath.

Taking the Derivative: Differentiate with respect to time (d/dt) to connect the rates of change.

Calculating the Rate of Change: Substitute known values to find the rate at which the area under the ladder is changing.

Why Watch This Video?

Ideal for Students: Perfect for high school and college students studying calculus and geometry.
Clear Explanations: Easy-to-follow steps that clarify complex calculus concepts.
Enhance Your Problem-Solving Skills: Build confidence in tackling related rates problems in various scenarios.

📈 Don’t Forget to:

LIKE this video if you find it helpful!
SHARE with classmates or friends who want to master related rates!
SUBSCRIBE for more calculus tutorials, problem-solving techniques, and educational content!

#RelatedRates #Calculus #LadderProblem #MathTutorial #EducationalContent #LearningCalculus #ProblemSolving #HighSchoolMath #CollegeCalculus #DifferentialCalculus #Geometry #RateOfChange #MathematicalConcepts

[patrickjmt]

Hi all! Wanna help a Youtube education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

[MrBoonka]

I found many people commented many things but I think Patrick solved the best way possible.
First draw the diagram, figure out whats happening and whats given, then form an equation, differentiate it
and at last plug in the values. So the important thing is there must be a general a general approach to every kind of
problem, that will help you to start the solving the problem rather than just sitting and starring on it....

[krookedboyz]

like if patrickJMT is better than khanacademy

[luisespa]

You did a great job explaining the exercise! Every time I wanted to see the problem by itself I just paused the video. Thank you for doing the videos!

[al]

Patrick, thank you so much for your amazing videos! I am SO glad that I found you when looking up how to do Newton's Method three days ago, before my AP Calculus AB chapter 4 test/final. I have been sooo lost in this chapter up until that point. Since then I probably saw 10 or 15 of your videos and it has helped me grasp Calculus like I never could before. Tomorrow I will walk into my Calc exam feeling like a pro and will get 100% on it all because of you. Thank you so much for what you do.

[kimblesxoxo]

Thank you! I think I finally understand how to do this! This video is so helpful and clear. The only thing is that around 9:00, when you switched from the 2nd to the 3rd paper, you left out the 2nd db/dt, which becomes 5!

[ceaderf]

The ladder question in related rates seems to be in every textbook on the subject so good on you for covering it.

[jackfinio]

The interactive transcript is one of the funniest things ive ever seen

[Alexj]

Do you have the on a the shadow of a really help!  
You are  a wonderful

[joshuahoeflich]

I solved this problem differently; I differentiated the (b^2 + h^2 = 20^2) equation to solve for dh/dt, which is about -2.182. Then, I plugged in dh/dt into our original equation. This made the differentiation substantially less difficult, and it was easy to plug and chug for a final answer.

[Sami-xcpl]

At 5:44 it is actually a product rule with chain rule. Not just chain rule. That part can be confusing if listening to you :)

[jimavellano]

we'll be having our midterm exam regarding this topic. thanks for the vid. it really helped me a lot :)

[emake]

I guess we have to do a lot of thinking when setting up on how to solve the problems involving related rates. But I'm watching all of your related rates problems and its definitely helping me figure some of this out so i can do well on my test on related rates tomorrow.

[curiosityplease]

Why didn't you differentiate the 1/2 at 5:35 ?

[cherdonparry]

thank you Patrick this was awesome and i use that DREDS method in my head and it really helps me also.. thanks

[stvntruestory]

i did this by finding what dh/dt would be and i still wound up with the same answer. i think its the same way it jus made plugging numbers in a little bit easier. i mainly use these for practice because you pick really good examples. thanks alot for the help though i know another way to do this that saves me a little bit of time. hopefully i do good on my calc final tomorro =P

[AnushkaLuvUrself]

lmao you help so much thank you for letting me pass all my calculus exams u the realest fr fr

[AnnieJoo]

BTW... you are a great math teacher!! I wish you can teach in my school....

[donnablankenbecler]

Hey! I'm taking calc right now. Thanks for helping me!

[MsOlkina]

I would break the solution into two parts. First I would find dh/dt by differentiating b^2+h^2=400 with respect to t. 
After that I would differentiate A=(1/2)(bh) with respect to t. (Do not forget the Product Rule).