Using the Chain Rule - Harder Example #3

📚 Finding Complicated Derivatives: Using Product, Chain, and Power Rules 🧮

Note: At the beginning of this video, there is a typo regarding the variable used; I should only use a single variable, either x or t.

In this tutorial, we tackle a more complicated derivative that requires the application of the Product Rule, Chain Rule, and Power Rule multiple times. This video is perfect for anyone looking to deepen their understanding of how these fundamental rules work together in calculus.

🚀 What you’ll learn:

A comprehensive step-by-step approach to finding derivatives of complex functions using multiple rules.

How to effectively apply the Product Rule when dealing with products of functions.

The proper use of the Chain Rule for differentiating composite functions.

Techniques for utilizing the Power Rule in conjunction with the other rules.

Worked-out examples that illustrate the entire process, ensuring clarity and understanding.

Whether you're preparing for AP Calculus, Calculus II, or just want to enhance your derivative skills, this video will provide you with the tools and strategies needed to tackle complex derivative problems confidently.

Don’t forget to check out my other videos for more insights into calculus topics, including implicit differentiation, advanced derivative techniques, and more.

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Watch now to master finding complicated derivatives using the Product, Chain, and Power Rules!

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[JO-fkho]

saving lives 7 years later. Thank you, sir.

[Nickrom]

I have watched a ton of your videos so far and you have immensely increased my understanding of this stuff. I am going to tell everyone I know about your channel! Thank you!

[gangstajpimpin]

I praise everything you do! You helped me pass my trigonometry class (PreCalcII) and now helping me with my Calc 1 class. Love it! Thanks and please keep making these videos!

[DmusikM]

Last minute studying for my cal exam tomorrow... you just made it ace-able, thanks for being so clear with your teaching (Y)

[patrickjmt]

@XTC2525 it was a 'typo' - i thought i added annotations, maybe not

[norac]

why am I paying tuition when I can get a better education on youtube

[Thorium]

when teacher explains, I feel as if I am in a NASA space station trying to understand the mission
but if the same thing is explained by Mr. Patrick, it becomes hell a lot simpler ! I enjoy those different colored markers, they simplify the problem into gas dude ! carry on ! and thanks for the chain rule :)

[patrickjmt]

@GoodyearBandit dont feel stupid, i typically left class confused.

[goodoldrebel]

Excellent emphasis about using the chain rule properly and not multiplying the -2 by the Cos at 2:25(in the video).

[rsgirl]

It's still correct. The answers are equal to each other. EG, 2/4 is the same thing as 1/2. It's not more correct to have one way or the other, but there are two reasons we simplify, that I'm aware of: (1) it's easier for teachers to mark (2) when mathematicians are proving things to each other and doing scary math, it allows for easier communication as it's prettier and less cluttered.

But if you're not worried about those thing because your teacher doesn't care if you simplify, don't bother =P

[patrickjmt]

@XTC2525 not in this video; this is first semester calc stuff.
i have plenty of stuff on partial derivatives and the generalized chain rule though.

[Ephesuz]

Thank you very much with this example. I have a test 4 tests this week and I had to focus on physics and chemistry and history. Due to you, I will probably get a good grade in maths aswell! thanks! 2 days left:(

[karambiatos]

Thanks a lot for your help, you actually now how to show people maths, my uni teachers are terrible its like they are teaching stuff they them selves dont really know

[patrickjmt]

@nikola1917 no, i did not fix it; is it just with the x and the t?

[dazzaondmic]

And I'd probably call that one a day haha

[pinksuedeshoes]

I can't thank you enough for taking the time to make these videos. I subscribe!

[patrickjmt]

@XTC2525 ok annotations there now. thanks for reminding me

[patrickjmt]

no one has pointed that out, and i did not even notice. i think i combined two problems into one, but did not notice the variables were different!! just pretend all the t's are x's or something!!! i will have to re-do this!! thanks for pointing this out : )

[anshchhabra]

You are the best Online Teachers Ever. :)
Btw, Can we Apply Log and Differentiate ?

I think that's easier, isn't it ?

[captainball]

"...longer or harder or even more miserable." Haahahhaha