Chain Rule for Finding Derivatives

[pyr666]

good review for my upcoming calc classes. yay internets

[unrivaled37]

Thank You SO much for this videeo!

[mmb314]

I just want to tell you how much I appreciate these videos! I hope you realize how much of a different you make - I would never have been able to pass my first semester of calculus without you. thank you so much!

[patrickJMT]

@mmb314 you are very welcome : )

[thetman22]

you helped hundreds of thousands of students succeed. You are a hero

[patrickJMT]

@thetman22 i am at least not the worst person on earth : )

[Slait0123]

Your videos are very helpful, thanks a lot!

[Laspher]

<3

[keplermission]

From the earliest ages, the constellations have exercised a fascination upon all thinking people; and their glory, and silence, and beauty have so enthralled the hearts of some, that divine honors have been paid to the starry host. Dr. Chalmers D.D. LL.D. (born in Anstruther 1780) was a keen astronomer who in a series of Thursday essays during 1816, expounded the wonders of "the eyes of heaven." His memorial lighthouse appears in the You Tube video of the Anstruther Scottish Fisheries Museum.

[amanslive]

patrickJMT what do we do with derivatives of number, also can you do some examples of taking derivatives of complex fractions

[xo1k4]

Will you please come be my full time teacher?? I don't have lots of money, but I can pay you by actually learning, becoming successful, and then giving you lots of money as a thanks

[patrickJMT]

@xo1k4 let me think about it...

[DevilChao5]

OHHH thats why we have the inside on the out. I never understood that till now!

[wh0iskarl]

seriously man. you and khanacademy :PPP

[patrickJMT]

@wh0iskarl now someone just needs to give me a few million dollar grant too :)

[Astindan]

Wow, thanks, this video helped me out a lot on understanding this topic.

[lucash743]

your videos are seriously the best, thank you so much patrick.

[SVUfannyc]

WOW MY TCHR just makes my LIFE COMPLICATED 4 NO reason!!!

sheesh THe thing w/math is I just Need tchr or whoever, to Just show me what to do step by step,NOT Blabber about x is this and that when this f(g(x)) crap & what not when limits is this and that....-_- IDK literal terms i Just know how to do things in math.! Thanks for ur help...certainly not my tchrs.

[rsgirl10]

Wow, here I was thinking it was a complicated version of the product rule. So glad I got that straightened out!

[MCwonRAus]

You are a legend!!!!

[Coolbluegirl77]

OMG YOU'RE AMAZING!!!<3 I had a C in Calculus until my friend told me to watch your videos and it helps so much!!! I have a B+ now and might actually get an A :)))) You're so smart & have such awesome handwriting!!!!

[Transane]

when you slid that paper down, for a second I thought to myself

"I KNEW HE WAS MAGIC! LOOK AT HOW MATH JUST APPEARS ON THE PAPER! MAGIC!"

Then I realized it was just a paper being slid down...

regardless, I still think your a magician.

[VevoBeaverJustin]

@VairrWasHere but you need tutoring so...

[christyzaki]

Thank you, you are the best !!!!!!!!!!! :)

[1029Memory]

Time to Ace tomorrow's midterm! Thanks alot bro.

[BKRandersProductions]

Literally everything I have ever typed in about calculus on youtube has come up with you as the first video. Thank you so much!

[JorgeHernandez80]

THANK YOU!!! :D



[silverflame92]

my friend....did anybody ever tell you that you are the best thing that ever happened on youtube..!

[chinchek]

free education, WHATS THIS?!?!? (thanks :D )

[Salamero500]

you're a life saver, thank you, very helpful.

[M0nk3yzGoB0om]

Rank 1 in my AB Calc class. thanks :D!

[QQLePewPew]

Multiply (x^2 + 3x +4) by itself 30 times? Challenge accepted!

[DancingMen11]

You're the reason me and calculus are still friends.

[teh1337hackz0rz]

Here's how Calculus has been going for me this year:

1) Go to lecture. Take detailed notes and ask questions.

2) Professor acts like I'm an idiot for not understanding. Answers questions for no longer than 10 seconds and moves on.

3) Attend recitation, take notes, ask questions. TA slightly more receptive to questions. Get pop quiz. Freak out. Fail.

4) Take concepts from quiz home. Youtube and watch Patrick's videos.

5) Actually learn stuff.

6) Get a pretty good grade on midterm.

You rock, man!

[patrickJMT]

@teh1337hackz0rz ha : ) trying watching videos on the topic your prof is going to cover before you go to class. you will get much more out of it!

[teh1337hackz0rz]

@patrickJMT I'd love to do that if he had any method to his madness. Two days ago, I asked him what chapters our quiz was to be over. He said "I don't know. Look at the syllabus." So I looked, and it says 3.6, 3.7, and 3.8. I studied them hard and I watched your videos on derivatives of logarithmic functions and I was so ready. The test was ONLY chapter 3.5 and I failed it hard. This class sucks.

[TimpBizkit]

@teh1337hackz0rz I can relate, I was embarrassed to ask questions I assumed the professor and 'everyone else' understood perfectly. Or sometimes I would ask, the lecturer would explain, I still didn't get it, and think "It's my fault for not preparing before the lecture, I'll just go and look it up on youtube afterwards, youtube doesn't care how many times I replay"

[TimpBizkit]

@teh1337hackz0rz I also have the experience of helping people at GCSE who 'still didn't get it' after breaking everything down into what I thought was a simple logical progression. It comes to mind Sheldon on big bang theory. If ma = mg what does that mean? For crying out loud Penny, a = g !!

[lizetteg7]

@teh1337hackz0rz This is totally me.. i can relate to you i am trying to do that right now.. got my final in a few hrs

[chisangaa]

you > my prof

[RexReedemer]

I love how my professor who carries a PH.D makes something like this seem so hard to learn. I thank Patrick for making it so easy to comprehend. Definitely will be doing better now on the upcoming exam

[Dr8co1]

@mdxfeever333 in class haha

[snailbacon]

thankyouthankyouthankyouthanky­outhankyou

[zzestyturkey]

i love you, man. i forgot i was doing calculus

[ccase2k]

Thank you sir, you never disappoint! 

[magazines823]

What if you have a value before the trig function? For ex -4sin(x)?

[snipersas]

well done. i missed a calc class today, this more than made up for it.

[FiresDoFly]

After watching this, it makes me think that teachers could become obsolete one day, when they can just hook up a projector with videos like this on it. Thanks for the help.

[patrickJMT]

@FiresDoFly it might just happen!

[tonyfazt]

@FiresDoFly

hell yeah -- get rid of high school all at once and just teach everymath course up to calc3 in middle school

they should make a TV channel where its all math problems and solutions all day all night like barney teaching you trig.

[grandmasternmk]

Thank you very much, this is very helpful!

[Tatezm]

Thanks a ton! That was awesome.

[GrimTurtle7]

You literally made me understand this in 4 minutes while my teacher couldn't make me understand in an hour and a half. Thank you!

[KhaosTy]

@mdxfeever333 IB Math HL Paper 1.

[lemmingsfly]

thanks so much you are so much more helpful then my senior citizen professor who skips over every step

[patrickJMT]

@lemmingsfly maybe he forgets!

[babycakes00777]

This is sooo helpful! And you explain it soo nicely! Thanks alot!

[patrickJMT]

@babycakes00777 happy to help!

[atlmacak]

very helpful thx alot

[jpmoench21]

YOU ARE SOOOOO AMAZING!! this helped me a lot.

[patrickJMT]

@jpmoench21 glad it helped so much : )

[MultiKRINKELS]

NOW I realized, I'm not dumb I'm just lazy . . . XD

thanks a lot to your vids the cool thing is I'm not bored with it AHAHAH

[patrickJMT]

@MultiKRINKELS yes, many people would do great if they had the same epiphany

[aolyahoo]

@MultiKRINKELS

I had that realization years ago, but recently made another: Being lazy was in fact a dumb decision. So Sir, you are in fact dumb, as I am!

[lapeeweeloka]

I took Calculus in college for the first time this past summer. I had only 5 weeks to master it and I aced ALL of my tests. I owe a lot of that to your videos! Thanks so much for posting them, they are really helpful!

[715chrisg]

Thank you very helpful

[doflegend291]

Thanks a lot for your help

[Morphae]

Fantastic, a really nice refresher on something that's pretty easy!

[skatty14]

Thanks! Took Calc. I, went to Calc. II and already forgot how to do this, you always cure me of my forgetfulness quickly! Merci! :)

[3croN]

Where is the chain ?

[matcpn]

Thanks so much for this. The book I'm using uses some impossible notation (dw/dx=(dw/du)*(du/dx)) but this makes it so much easier.

[Cancer98765]

I have sin(x^2) as a problem go here to figure out how to solve these as a general review and see an exact problem I have lol!!!! You are that perfect o.0

[YoSuaYoSaN]

you're lefty :D

[sil2k8]

@mdxfeever333 If you're working with Astronomy.

[despicablerainier]

my prof. always teaches us the hard way, >:,(

[southernbelle121972]

Thanks for helping clear this up!!

[1717oranges]

you're AWESOME!!!

[aquacoolchick4]

Thank you sooooo much!! I have NO idea it could be explained so easily. :O

[YouPeople18]

@mdxfeever333 To figure out how many burgers you'll be flipping today, plebeian.

[supersal001]

I think i just broke the record for the fastest app download, i did not even finish reading the annotation in the video about the app, when it was already downloading

[Scottde911]

Thanks for all the help! Its nice to have these video's online. =)

[scrubsguy101]

Thanks man! your vids are awesome, simple and in-depth which is usefull! thanks

[MeSooCrazyy]

Thanks a lot !I've read a chain rule on Wikipedia but was like What is that ??^^ lol

[supersal001]

@MeSooCrazyy I was more like: WTF is this S*&T!

[MeSooCrazyy]

@supersal001 yeah,haha

[grico88]

patrick... I lOVE YOU, I got a 74% on my exam because of you if you ever come to windsor ill hook you up

[amkrro2]

thank u solved my problem in 2:min n 2 sec

[enlargemedia]

When is it better to use the chain rule versus the power rule? Or is there a specific case for each?

[Chemlea]

confused =l howcome for the function sin(x^2) we use the chain rule and not the product rule? thanks!

[dajakesta1234]

dr. professor patrick if f(x)=sin(x) wut does f '(x) equal?

[desertfox1792]

@dajakesta1234 cos(x)

[sk8erbassman]

Very good vid. Well Done!

[MendoBud640]

thanks for posting, very helpful.

[SoloeDj]

Duuuude so helpful thanks alot !

[ShrimpCrackR]

Hi, how can you tell which rule to use? for example y=sin(x^2),,it seems like you could use both the chain rule and the product rule because it's multiplying. Or will the question always specify which rule to use? Thank you!!

[pkflyers]

@ShrimpCrackR

in that example, you will use chain rule..you only use product rule if you are multiplying two different functions, like for example you would use the prod rule if u wanted to find the deriv of y=x*sin(x^2)

[DeeJayFoodstamp]

@mdxfeever333 when you balance your checkbook ... d'uh

[Splooshiba]

@mdxfeever333 on your university math test. boom.

[techstoner]

awesome thanks for helping

[saintpetersburgers]

isn't the derivative of cosine actually negative sine, not positive sine?

[saintpetersburgers]

isn't the derivative of cosine actually negative sine, not positive sine?

[Nick153452]

Calculus doens't work.. At least the way my calculus book explains it.

[Juriello]

Interesting. . .thanks a bunch!

[chittychad18]

I would fly to your house and kiss ya! I learned more from you than I did from my Arab Einstein teacher!

[moozchi]

Your videos really saved my grade, thank-you SO much!

[Zoidberg227]

Thanks for the great review! Haven't had to think about the chain rule for a while, so I'm a bit rusty when it comes to this stuff.

[sasusaku21]

Wah! Thank you so much! :'D This really helped me! *was totally stuck on this one problem for more than an hour*

;__; If only I knew it was this simple~

[futuretaco]

my brain hurts

[pannoni1]

Why do they have to have ADS before this educational stuff? BS, I'd rather just go back to my CD-Roms and paper textbooks without worrying about the world of consumerism!

[baboylove]

THANK YOU VERY MUCH, YOU SAVED MY LIFE.

[pyVlad]

Hmm... I'm pretty sure this is right, but I'm checking just in case. In differential notation, is the chain rule written as:

dy/dt = (dy/dx)(dx/dt)

(If y is a function of x, and x is a function of t.)

[shell9332]

wow ur videos are soo helpful!

thank you!!

[patrickJMT]

@mdxfeever333 if you take your money to the bank

[hamzakhan111]

@patrickJMT haha clever

[hujnbds]

@patrickJMT i wish

[Tripp393]

@patrickJMT Ha! The joke's on you, I don't HAVE any money.

[milkeatscereal]

@patrickJMT if ur a gazilionaire

[KevothatGuy]

what do you mean by evaluating the term?

[jeveuxlesoleil]

LIKELIKELIKELIKELIKE.

When you wrote down the fcn after 2:30 I literally squealed with happiness. I have one of those on a midterm review and the exponent at the end was driving me nuts. I was overthinking it entirely. Thank you SO MUCH!

[Irinagheorg]

Great idea with this kind of videos!

[bekeeper26]

@patrickJMT Tomorrow is my last calculus exam before the final. I've watched like 4 or 5 of your videos and now I finally feel as if I can do well. :)

[cadmusdixon92]

Thank you!

[iwtgia]

oooh if only you were my prof., i would be much more apt at learning...;____;

[therock343]

If only the Derivative on tests were this easy... I had a problem on my Calc test Soo long it took up a whole page just to show the work.... I was freaking out trying to keep up with my own Chains (if that makes any sense) ...lol..Got 90 on the test though.

[patrickJMT]

@therock343 well, this is meant to be a basic introduction to the chain rule, not the hardest problem ever. i do have harder examples using the chain rule if you wanted to look for them.

[dustinchen]

@patrickJMT you should give it to him, since he's bragging (90 on the test)

[MattyHild]

@therock343

Enough with the math-penis waving.

[almaca10]

I liked it a lot! the way he explains is so simple, congrats! I understood! =)

[3LiFu3nT35]

oh wow it's not so difficult after all.. thank you soooo muchh :)

[mrhe832]

My AP Calc AB class meets every other day and is 90 minutes a period. I spent nearly 75 of those minutes doing the chain rule, and barely understood what the hell my teacher was talking about.

You showed me how to do it in under 5 minutes.

Thanks so much!

[darkrifle]

DUDE U ARE THE BEST, if i watched this vid b4 my MId sems I would have passed....and it just takes 4 and a half minutes!

[kallie34]

I LOVE YOU.

i have a midterm in two hours.

i owe you my life.

[TH0RAXXE]

Oh my god, I now understand the chain rule. Thank you.

[alfiechung]

man. u have helped me for like.. so long now.

text books and professors just confuse me, i love the way u explain it so simpily without all the alien language

[carliefischerful]

i actually love you.

[123adrianramirez]

Your explanations are great! But how would the question be for such a problem? It wouldn't just mention to use the chain rule would it?

[Sums420]

you are saving my mark in university dude haha

[jahgrizzly]

Your explanations and break downs of these lessons are extremely helpful.. Keep 'em coming!

[kaneetacourt]

Professor sucks compared to you man

[charsi420]

thx dude love these videos :D

man i love college,, chug chug chug chug...

freshmen, freshmen,,... do something crazy, do something crazy...

kegstand... kegstand..

[Seedofwinter]

Why doesn't the chain rule work with this problem: f(x)=9(x^2-3). The only way I could get the correct answer is by multiplying the 9. The chain rule should work for this, no?

[Riverain96]

@Seedofwinter No, because 9 has technically only been factored out here. You dont ever take the derivative of that 9. You only take derivatives when the number is either a variable (the x^2 in this case) or a constant (the -3). You can see this if you multiply out the 9 before doing the derivative, then you realize that factor of 9 never gets differentiated.

Heres the example:

f(x)=9(x^2-3) then f'(x)=9(2x) which simplified is 18x

[Seedofwinter]

@Seedofwinter Yeah I finally realized it yesterday. Thanks man.

And the chain rule does work; it's just that I forgot that that inside goes to one, since it is raised to a power of 0. That's what i neglected.

[shomone]

Ah! All I want is buckets full of money, why? WHY?! Must I do all this work!!??

[TheRab1993]

thank you so much, in cal now and sooo lost

[Sujjisama]

Thanks a lot for all your videos. You're great!

[eclipse245]

okay...I'm in Advanced functions. i don't understand what derivatives give you? All it looks like is like you're still left with a super long function?

[konryu123]

i <3 your videos!!!! im taking ap calc bc (calc 2) and these videos are a great refresher the period before a test

[thehoaxbuster]

Patrick. I love you.

[Johnjpcoc]

dude u are the bestttt...... fucking Den i fucking hate u....

did u hear meeee fucking face.... u are a fucking dumb teacher i ever saw in my life...

douglas collageeee,,,,, vancouverrrr.....

[Lrichy11]

i get all of this except when there is e thrown into the mix, for example

y = (e^3x) / (1 + e^x)

what is the outside function and what is the inside function and I know that the derivative of e^x is itself but what happens when a three is thrown into the exponent and etc. another problem i have is when e^-x^2, like when the exponent has an exponent, what happens then?

[eordogadam]

Math is more hardcore than Fuckfaces!

:D

Thanks for the vid.

[lyflorida]

Thank you.

[MikSane]

you sir, are a fucking hero to me right now.

[warh34d]

This man is hero.

[diornotwar123]

Ahhhh, this helps A LOT!!! Makes so much more sense when someone else explains it. I'm taking calculus through correspondence, so I'm basically teaching myself. Thanks again!!! :D

[park4488]

Thank you jesus

[memsb1]

You see, that took 4 minutes, not hours of complex proofs that only serve to further confuse you. If the rest of your videos are this clear and simple my life is going to get a lot easier!

[arturomlk92]

@memsb1 I agree proofs confuse me and in the end are useless.

[patrickJMT]

@arturomlk92 to say they are useless is to go to the other extreme. they certainly are not useless. however for most students they do end up being irrelevant.

[arturomlk92]

@patrickJMT Yeah, I mean if it wasnt for the proof technically it would be false and wrong but the proof never helped me. lol By the way your site really helps with studying. I have a calc test tomorrow.

[BXNYhardstyle]

FCUK MATH

[patrickJMT]

@BXNYhardstyle ya boy, you tell that math!

[patrickJMT]

@BXNYhardstyle you too hardcore for math!

[sakkarugzo]

@BXNYhardstyle

Say that when you are on airplane.

[MrBlackfish011]

@BXNYhardstyle guess your flunking english too huh?

[lifematch]

@BXNYhardstyle french connection united kingdom (FCUK) math? i don't get what ur trying to say?

[griffonstomp]

yay for lefty

[MoT359]

thanks man, my professor is sooo asian this semester, i cant even understand him.

[Zerghumper]

Thanks for posting this, I'm taking an online class and my book is incredibly unhelpful. Do you have text versions of your lessons available as well?

Thanks so much!

[dcheng115]

wow, you have amazing handwriting haha. great video too.

[mvenom101]

Yay for free maths tutoring :)

Im in australia in high school, and this helps soo much. so, now i can spend more time riding my kangaroo to school, and hugging koala bears.

:)

[patrickJMT]

@mvenom101 i grew up in kentucky. i had to walk to school barefoot, get water from a well, and use an outhouse. 

[flyingporcupine2]

@patrickJMT goes to show americans are complainers

[patrickJMT]

@flyingporcupine2 yes, every single person in usa is a complainer. everyone else in the world is sweet and wonderful.

[Seedofwinter]

@mvenom101 LMAO You're trying to be funny right?