Using the Chain Rule - Harder Example #3

[unrivaled37]

thank youu!!!

[TheHande4]

I didn't get what you meant in the blue box... :/

[goodoldrebel8]

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

[teardownyouridolss]

5t^4...still chillin' out 

[lifeDotGov]

what happens when theres infinite chain rules 

[patrickJMT]

@lifeDotGov the universe collapses on itself

[GoodyearBandit]

I FEEL GOOD! i understood it All, in class i felt stupid.. :(

[patrickJMT]

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

[bikeous23]

These videos are very helpful, thanks for posting!!

[knotnyce]

Patrick you are one of Earth's everyday heroes & u dnt even realise it =)

[xdarkdragonx01]

do you have video on chain rule with partial derivatives?

[patrickJMT]

@xdarkdragonx01 general chain rule

[bodinian]

We want you to give it to us longer and harder.

[XTC2525]

no partial derivatives???

[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.

[XTC2525]

@patrickJMT then why write a function in terms of 2 variables? someone in first semester calc would never see a function in 2 variables unless it was some advance first semester calc class or something

[patrickJMT]

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

[patrickJMT]

@XTC2525 ok annotations there now. thanks for reminding me

[nikola1917]

did you fix this one? per a comment on here you did it wrong and said you were going to fix it? just don't want to get confused... =)

[patrickJMT]

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

[pedjasta]

looks nice but unfortunately it is not correct to derivate with x and t in the same function :(

[patrickJMT]

@pedjasta just a typo

[m00nlight13]

this is great, i was getting confused if i should do the product or chain rule for sin(1/x) thanks!

[KAYaKHA]

STILL CHILLIN OUT

[Iplayguitaramazingly]

You're a life saver for my ap calculus class...you teach soooo much better than my teacher...I finally get it!

[darlszz]

thanks :)

[arsevela33]

longer and harder haaaa thats what she said lol

[sakanmn06]

please do another more miserable and more exciting example...

just one more time..

[stineqt]

" Then we still have 5t^4 just chillin out.." Hahah you even have time to add in your sense of humour during your vid. LOVE IT.

All your videos are extremely helpful! Thank you!

[alanezi1200]

thank you sir and i am from Saudi Arabia and i want from if you allow more examples about implicit and chain and log derv

thank you

[MiThRaZoR]

Thanks!

[eldiosdedios]

Still chillin' out FTW!

[blackdefender]

I liked the intro..yeah, I agree, can you make more videos? It would really help us a lot! Your way of teaching is superb! Thanks for the help, always! 5/5!

[junquan855]

This would be slightly misleading for some people although u are really just demonstrating the chain rule. It should be done using partial differentiation because y is a function of 2 variables.

[sponsoredwalk1]

That's true, those "t"' values should be x values, if t was held as a constant the whole second term would just drop out, otherwise two seperate partials should be done.

But, as this video is just for demonstrating the chain rule it serves it's purposes.

It does illustrate how we can blindly assume to differentiate with respect to "t" just because it's commonly used, I did this problem myself before watching & I also treated both x & t as variables.

Never making that mistake again :p

[kunka4241]

6:18 THATS WAT SHE SAID ahahah

[XxTNTxX92]

since you are doing df/dx, doesn't the part with the t variable becomes 0 because d/dt (t) = 0?

[mycelthedudex]

Dude,,,,,thanks a loooot.....You rule bro....your vids are great....yes please, it would be great if you would make us suffer with videos that are "longer and harder and even more miserable" hahaha....please do....^^

[milkeatscereal]

@mycelthedudex thats what she said XD

[Tehhunter1]

Hey Patrick don't you need to change the sin's to cosin's and cosin's to -sin's? I think you made that mistake in this chain rule example.

[mycelthedudex]

no dude,,,he did it correctly....review it a couple of times...you'll figure it out...try to do it yourself...it will come clear that way....

[TSSolaris]

u are an idiot

[pbcmercrat]

wah! why isn't your website up!!?

[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!

[weweallthewayhome]

are we not treating the "t" as a function?

[nyah012]

I believe the problem's simplest answer would be, instead of having a -6, going back to the blue brackets and cancelling the 2 with the 1/4 of the stuff before the blue brackets. These brackets would be [(-3+9t) + 5t^4]

The answer would be

sin (1/x) - 1/x cos(1/x) - 3-9t-5t^4/2[(1-3t)^2 + t^5]^3/4

or something like that?

[MetallicaFTW7]

oh my god.... i swear these problems are the freaking longest problems..... lol

[cchapar]

Hey, i just watched all 3 of you're complicated chain rule vid's, but if you get a chance, making a video w/ natural logs & the chain rule would help. Thanks.

[ohmannhey]

Why are you diffirenciating with x and t in the same function? On what are you diffirienciating x or t? Can you do it for two variables?

[vrolok4768]

Clap clap clap clap

Very good! I finally understood the chain rule, thanks!

[minnela]

Woah i might not be clever but that right there is hard i can see that

I dont even know what the commenters are talking about

[mannyiscuddly]

lol more miserable? kinda sounds like you're enjoying yourself :P

[cchapar]

rofl, i think ur right. but I believe that's the reason it's all so easy to understand when he explains it.

[RusselPfan45]

A chain rule problem parametrically would be nice. dy/dt divided by dx/dt. Where y, x, and t are all given to you. And you want dy/dx. I'm actually working on a problem like that now, but its relatively easy. A hairy parametric problem would be nice to see though. I'm having a little trouble with the more hairy problems.

[ma3828]

excellentttt

[ma3828]

that was a rough one, I like it

[ChristynA2]

This is so awesome!! I totally get it now!

What I can't get is...

e^(7x^3)(xlnx)^3+2(10xe^x)^4..­.so if you were to get any time...help me out plz = ]

[vdn130490]

mnogo si dlakav po rukama za jednog profesora, moj profesor ne skida sako sa sebe pa i neznamo sta je ispod, al posto je bivsi kosarkas verovatno je ko osmudjen... tako da brij se

[vdn130490]

ajde ajde nije tu nista tesko, samo plasis ljude... kad sam ja imao 3 iz toga...

[jacobbis4lovers]

Holy crap, I wouldn't even attempt to solve that problem even if it was on a test. I'd get it wrong even if I tried. Fuck that shit.

[patrickJMT]

you are just that hardcore

[jacobbis4lovers]

I don't think I would have to take a calculus class anyway since I'm really bad at math, but I still think this video is great. I like your algebra videos better, though.

:]

[logical123]

@patrickJMT I just realized that it's actually very easy, the only problem is not getting lost.

[lenahmata]

@patrickJMT

[Callohcallay]

good job, its fun to solve the problems, really helpful, good job!

[dmceye]

no problem, im just trying to redo some of your questions to study for my midterms tomorrow night.i

[dmceye]

Very helpful video. I just have one question, Why didn't you differentiate the variable t implicitly? since you are differentiating with respect to x.

[patrickJMT]

oooooooohhhhhhh wooooooooooooooooooow!

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 : )

[chrisdkpl]

very helpful, thanks dude!

[MundusLitterae]

lol you're right I love the chain rule :D

[patrickJMT]

who doesn't?! : )

[snakemeister]

you are awesome, great vids....more more more chains :D

[patrickJMT]

thanks friend!

[brco2003]

Great vid's, Pat. I was wondering if you're going to be doing any multivariate stuff... like partial derivatives and multiple integrals and the theorems of Gauss, etc. Also linalg stuff?

[patrickJMT]

i have vids about partial derivatives and double integrals on here! : )

[brco2003]

Oh, awesome. I found two of them and they were excellent. Thanks! Are you going to do stuff that's slightly more advanced like vectors?

[patrickJMT]

vectors... one day!

[AznHavx90]

"longer harder and more miserable" ROFL

[patrickJMT]

: )

[atomo360]

you rock patrick if you keep this up your reputation of a math god will grow and that means fame and chicks haha take care

[patrickJMT]

hahahahh i dont know if math people get famous... and my hot math phd wife will not like the other math groupies! : )

[FarFromEquilibrium]

thanks XD yes *longer harder more miserable* sounds perfect!

[patrickJMT]

: )