More! Implicit Differentiation Examples

[2PACAC]

my b just read the bottom comment someone already said it

[2PACAC]

i think you made a mistake for your 2nd example, the derivative of y^2 is 2y not 2y^2

lol

[josh08h245]

thanks to you, i should be getting into my uni.

[patrickJMT]

@josh08h245 good luck and congrats!

[H0oLIgAnSsRo0lMaRrSz]

so would the slope intercept equation be y=-x+2??? somebody plz answer?

[PullarBearBear]

@H0oLIgAnSsRo0lMaRrSz Yes. At least that's what I got too. :D

[thecocabonga]

I wish some teachers could explain stuff as you do! Great thx for the videos you provide.

[flyingsquirrel104]

I bet you hear this often, but thank you! Your different perspective on math concepts (at least compared my professor) really helps me understand. Thanks again!

[studentofthemind23]

i think you did some math wrong. in your second example, the derivative of y^2 should be 2y times y prime not 2y^2 times y prime. you have to subtract the exponent by one when you bring it down. I might be wrong but I don't think I am.

[systemX50]

@studentofthemind23 no, you're right, I definitely noticed this

[systemX50]

@studentofthemind23 the math works out to be the same though.

[assassin465]

I wish I would have looked at this before my AP Calc test! SMH

[nickdisciullo]

hey Pat, my girlfriend is ... how do I say this... challenged with this stuff. your videos helped a TON! if she can understand you, ANYONE can understand you. And she now wants to leave me for you.

[NicholasJNadon]

Thanks for mentioning the mistake! :) I paused and solved it before continuing. And then I thought my answer was wrong.

Thanks Patrick! you rock!

[Libservative79]

I <3 you! I have a calc midterm tomorrow and I really didn't get a good, in-depth explanation from my professor. Seemed like she didn't understand why you apply dy/dx to the equation. You rock (despite the derivative slip-up with the y^2) ^_^.

[Timberwolvesfan25]

the derivative of x in these type of problems is 1, right? just making sure

[patrickJMT]

@Timberwolvesfan25 if you are taking the derivative with respect to x (which we are) then that is correct.

[shenalv]

Thanks for the video,but what do you get when you differentiate 2y????

[dotdelusion]

@shenalv Yeah, shouldn't you just get 2y (dy/dx) ?

[thechelsseeaa]

your videos are great, i just wish you weren't left handed.. hahah you keep blocking what you write :P

[shellumiel]

Thank you so much i really understand this now. You are the MAN!!!

[TheDougheyMan]

i feel like i just saw ur username on xbox

[patrickJMT]

@TheDougheyMan if you did, it is for sure not me.

[silverflame92]

YOU ARE SO WRONG....your website's name is patrickJMT(dot)com

not 'justmathtutoring(dot)com' like you showed in the video..! :P ilike the new domain name better!

[amaclellan3]

whats the derivative of just y, dy/dx?

[silverflame92]

@amaclellan3 yup.....its 1 but when you take a der. of y you MUST put dy/dx

just like patrick taught us..!

[wperlich]

24 year old "back to school" student here. Got an A on my first calculus test thanks to your videos. Hope you're around for integrals next term. Thanks.

[patrickJMT]

@wperlich tons of calc 2 stuff in my playlist. i am not going anywhere any time soon. : ) congrats on your A!

[coffeegal4life]

shouldn't you have taken the derivative of 1 on the other side? (1+x) part.

[SofiyahSapphire]

@coffeegal4life the derivative of 1 is equal to 0 so it was therefore omitted

[MendicantBias69]

calculus with a sharpie?! you are one wild dude.

[DrTacoWaco]

your a math wizard!

[Outrageouss2]

I FINALLY GET IT! YEAHHHHHHHHHHHHHHHHHHHHHHHH

[TheEliteBboy]

You're the man! I'm gonna rock this test tomorrow. You took the wrong derivative of "y" though. Other than that, goooooood stuff.

[silascb]

If my Calculus teacher told me that the world was going to end tomorrow, I wouldn't listen to a word he said. But if you told me that the world was going to end tomorrow, I'd believe everything you say because I know you know your shit. If only I had found you years ago, or even a week ago, I think I'd be able to do better on my calc midterm today. Thanks! I'll check back in for the rest of the semester! :)

[ThundaSundaa]

lol you are honestly like my math teacher now.....cuz my teacher SUCKS, and when u explain it i actually UNDERSTAND haha thankkk youuuu :)

[ohlyshiet]

I LOVE YOU SO MUCH I UNDERSTAND IT, AFTER 2 HOURS OF REPEATING YOUR VIDEOS AND EVERYTHING OMFG THANK YOU!!!!

[hyametal]

@patrickJMT i was just asking cause i want to pass calculus no need to get all sassy on me

[patrickJMT]

@hyametal that was not sassy.

[sulmazz]

@hyametal please refresh your definition of sassy -

[hyametal]

the derivative of y^2 should be 2yy' should it not?

[patrickJMT]

@hyametal yes as the annotations and hundreds of other comments point out

[ChrisLikesMusic92]

i'm a lefty and i wish i had nice hand writing like that ._.

[Fruitie4U]

I must say that you have truly made my worst class into my favorite....Thanks!



[Fruitie4U]

I must say that you have truly made my worst class into my favorite....Thanks!

[cupofrice]

You are a math god.

[patrickJMT]

@cupofrice ha ; )

[kingallen08]

You are my teacher from now on



[patrickJMT]

@kingallen08 i am always here : )

[6193031]

very well done i,m learning something

[cheatroy055]

on the second problem, the derivative of y^2 is supposed to be 2y right, not 2y^2

[aditya9724585849]

AWESOME VIDS...I NVR THOUT DT.. YU WUD MAKE IMPLICIT DIFFERENTIATION DIS EASY..ITZ NW FUN 2 SOLVE IT..TNK YU..

[marm742]

thankyouthankyouthankyouthanky­outhankyou this has been exactly what i need! you explain it like a hundred times better than my idiot professor does!

[hannah1214]

for the first problem, on step 3, i don't understand how you pulled y^2 out but still have cos(xy^2)!??!?!??!explain please!?

[khwezi1986]

will I be wrong if I devide the 1 with cos(xy^2) and then work with sec(xy^2)=y^2+2xy.y' and how come u have a y^2 in the second example

[khwezi1986]

will I be wrong if I devide the 1 with cos(xy^2) and then work with sec(xy^2)=y^2+2xy.y'

[AntonMostertSA]

What a guy



[JizzKing8542]

I love you. Thank you so much. This helped me so much with preparing for my test.

[omgpwnd]

After going through a term with one GTF teaching me, a second term (I failed the first one) with a different GTF, and the khanacadmy videos for implicit differentiation I was still struggeling. I don't know if it is just the way you explain it or what but I'm understanding much better now. Thanks Patrick.

[patrickJMT]

@omgpwnd my pleasure - glad i was able to help

[RISEofTIBET]

@patrickJMT hi shouldn't the derivative of y square in the equation be 2y times the dy/dx rather than 2y square times dy/dx? i am referring to the last part of the taking derivative. as always thank you Patrick...

[patrickJMT]

@RISEofTIBET yes, i think i made a mistake in this video if i remember correctly!

[MetalNeon]

@omgpwnd

What's a GTF? :p

[Jesz023]

at the second example, luckily, 1^2 is still 1..

[419764]

why isn't there a sin at the end of the first dydx on line two?

[hunnybear20]

My official, new youtube legend :')

[koenigsegg1000]

wouldn't y² become 2y dx/dy? 100% sure this derivation is right and the one in the video is incorrect.

[koenigsegg1000]

@koenigsegg1000 i mean dy/dx

[tech4rce001]

i dont know what to say !!! you are not my teacher, but you are proffessor!! thanks man , my exam is tommorow and this video helped me alot !! ( not mention there is a mistake in the video )

[RidaMalik1]

Thanks Patrick... I had bad dreams about implict differentiation before I watched this video. My exam is tomorrow and thank you so much!!

[gadgou2]

i simply love you, this was exactly what i needed to know

you're definitely number 2 person who saved most peoples' lives (Jesus being number 1)

xD

[thisisarandomname92]

Ur AWESOME!!!

[evangill15]

its 2y DY/DX not 2y squared DY/DX.

[MssAnissa91]

what if the middle term was to be 2xy, instead of xy..

i don't know if what im doing is correct..

so the problem would be

x^2 + 2xy + y^2=3

[SirThursday3]

9 people wish they were as good at math as Patrick...

[uza10101]

I think there is a mistake the differentiation of y^2 is 2y not 2y^2

[bbtam]

simply genius

[aniutastr]

OMG!!!!!! Patrick!!! you saved me!!! thank you so muh for your videos! i started doing the HW and i was just stuck on every single problem! i didnt get it at all! not, after watching your videos i did everything! thank youuuuuuuu! very much!!!!!!

[patrickJMT]

@aniutastr perfect : )

[bustachaina]

wow omg you're such a god! i love you so much! i did NOT get implicit diff. at all. this stewarts book is so hard to get sometimes, im just not as smart as you. but this helped so much! i also thought i was the only one who watched your vids but the other day in class i heard other classmates say "go watch patrick" with others chiming in "yeah he teaches everything in like 2 min . so easy" <3 you!

[patrickJMT]

@bustachaina ha, glad you and your classmates like the vids : )

[choji1212]

I got thrown off cuz youre a lefty.....>:(

jk

[apira21]

can't believe this seemed so complicated in class...thank you sooooo much! makes complete sense now :)

you're an awesome teacher! i'll definitely be directing other people to your vids.

[bvlgary09]

Okay i'm back for more cramming the night before the test:)

[one0xin]

thx Patrick....i've been hating implicit and dreading to take the test...but now i feel confident enough to take my test tomorrow!!

[patrickJMT]

@one0xin good luck on the exam : )

[mjmclr]

did you answer reggie's question?

[mgainer1]

I bet your asian but it doesnt matter ur amazing just the way your are omg thank you so much

[4givensinner]

@mgainer1

Asians doesn't have that much hair! Nor are they that pale of a skin color.

This coming from another asian. Haha

BTW love your vids!

[DrBandgeek156]

Compared to my calc teacher at school, your lectures/teaching skills soar WAY beyond what he is capable of doing. I understand EVERYTHING whenever you explain, whereas my teacher confused me on the first day when we learned limits...

Thanks for being here Mr. Patrick! xD

[cbarragan9]

why can't you be my math teacher?!? thanks! you really helped a lot!

[MajinAmmaar]

I've lost faith in my professor, in class I find your video on the subject we are learning and go home and watch it. I love this, thank you so very much!

[epsotoma]

Patrick!! im having the worst time with this problem!! how do you do this?? pleaseeee help me outt!! i dont wanna fail my cal 2 exam!! :(

Use implicit differentiation to find an equation of the tangent line to the graph at the given point.

x + y − 1 = ln(x^18 + y^6), (1, 0)

[sexxyjenne]

thanks so much!this helped a lot! God Bless : )

[angelusp777]

you need to know two main things

u(dv/dx)+v(dy/dx) and (dy/du)(du/dx) other than that you need only to know

cos > -sin

sin > cos

e^x > e^x

x^y=e^lnx(y)

with these you can derive almost all.

[1990loveanna]

Thx.. U really help alot :)

[2060Tinkerbell]

The way explain math totally makes sense. Can you please post some videos on implicit differenciation of the ones with Radicals/square roots pleaseeeeeeeee.

[timetrialtom]

learning all the maths i can for my oxford physics aptitude test in november lol.

[like9orphanz]

Anyone who dislikes your videos should go to the chopping block

[derr69]

do you just put in the dy/dx every time you have to differentiate y? that was my only question about the problem

[ilikeche2]

that sound in the background is infuriating D:

[miki1king]

duude can you just come and be my teacher? i learnt more in 9 minutes than what i have in a year!!

[lmfaowtfinghell]

mannnnnn i keep getting confused with when to use the chain rule >_< AHHHHH.

[iyanneech]

I agree,. It should be 2y not 2y^2.,. By the way, I like ur 1st video, thanks.,.

[linkinms]

Thanks so so much.

God Bless you Patrick!

Will donate with what I have right now as a thanks :)

A cheer from Saudi Arabia :)

MS

[bencalejackson]

This will no doubt help me with my exam monday, thanks dude

[indifel]

can you please fix ur microphone?

there is this continous hissing sound in the background, quite distracting, and especially with headphones on.

a million thanks for the videos :)

[fewetoo]

Dude, you double rock. I pretty much go to class to get homework assignments. You are the one who actually teaches me this stuff.

[dragonmasta91]

i am paying thousands of dollars for calculus classes which i dont get, but i dont even pay a single amount of penny to watch videos, that are actually helpful. Thank You for all your help sir.

[sbejin]

i found your method of teaching very helpful. thank you sir

[sbejin]

thank you

[CrypticWatcher]

At the end, can you cancel out the cos(xy^2) on the left?

[gamer0reloaded]

@CrypticWatcher no you can't bc you're still subtracting in the numerator

[logicaust]

This helped me out of a hard place. Thanks for the clear explanations about what each step achieves etc.

Needless to say...I'm going to need to do a lot of revision.

Peace.

[zeidakiss]

you deserve a beer.. thanks brutha

[patrickJMT]

i am drinking one right now after a long day of work... it is gooooooooooooood

[olliivier3]

@patrickJMT I'd say, grab yourself a belgian beer. Your work is appreciated over the atlantic also !

[T3hbuddie]

Woo, you're left handed. :)

[xxxxxreggiexxxxx]

there's an error in the second example... the derivative of y² is 2y... not 2y²...

[indifel]

@xxxxxreggiexxxxx yeh ur right, should be (2y) dy/dx, not (2y^2) dy/dx

[patrickcommiskey]

@xxxxxreggiexxxxx Youre right man

[jingcarlolaya]

Thank for the lesson sir..your a very good teacher..you sure did help me.

[kjanis10]

on the last term on the left side of the equation (y^2), wouldn't you differentiate it to 2y dy/dx instead of 2y^2 dy/dx?

[myez]

Yeah, he already addressed that via the annotations and replying to all the people who saw that a year ago.

[kjanis10]

oh .. right.. my bad

[heyyhowyadoin]

dammit patrick. the pope should make u a saint.

u ask for nothing a give everything

[patrickJMT]

ha - just hedging my bet in case i make it to the pearly gates

[heyyhowyadoin]

im sure you will.lol. everyone needs a good math tutor.

and mechanic and lawyer and doctor.

[karlkarlkarl1234]

Patrick, do you do some other mathsy work other than teaching; like engineering, physics or computer science? Or are you all about the pure math?

Just curious for some reason, possibly as I sometimes dream of emulating such a position.

[dragomanrd2]

dude if you ever read this i just wanna thank you for getting me through my first university math course. you are a scholar and a gentlemen

[patrickJMT]

very happy to have helped

[zskarimi]

You sure did help me! Tnx sooooooo muchhhhhhhh :)

[zskarimi]

You sure did help me, tnx soooooooooo much :)

[awkwardmoment3]

Yay for lefties!

You're awesome man. Keep it up!

[patrickJMT]

lefties pwn

[755hp]

Hopefully (with practice) I can be as good in math as you are............I need it for Engineering!!

[patrickJMT]

i worked my butt off - that is what it takes!

[skyfaze]

ur gangster man thanks

[hanjuneul]

I was extremely intimidated when I saw that we had to do implicit diff. for calculus, and i was having a difficult time on the hw! But after watching your tutorials, solving implicit diff. problems has become somewhat fun O_O;;;....so I thank you so much, Patrick! you're an awesome teacher! please keep doing what you're doing =`D

[Hamza8as]

i have just noticed a mistake.. in the second question u solved.. the derivative of y^2 = 2y but u've writen it at 2y^2 ..

[hrixenz]

excellent

[cchapar]

rofl. nice work and thanks, this really helps.

Haha you're a slope-intercept racist!

[iamashooter]

you are really neat

[eackpal]

eackpal

[kashiark]

what happened to the three?

[gothikwerewolf]

it was derived out lol

[hakoonamitata]

Your videos are definitely going to contribute to the numerator on my test tomrrow :p

"be like a normal lazy math person and save yourself some effort" LOL

i've never seen that form of equation btw, y-int is all i've known -- good to know!

oh and THANK YOU =D

[hasbren90]

Thanks for posting all of these videos. They are great refreshers, and your style of teaching is clear, concise, and easy to understand.

[rugby1765]

why dont you cancel out cos(xy)

[hasbren90]

you can't because it's 1-y^2*cos(xy^2) on top... you can't divide out the 1. However, you could do 1/denominator - y/2x if you really felt like it. I'm not so sure it would be simpler though--

[draftube]

Can't you make it:

dy/dx = (sec(xy^2)-y^2)/2xy

?

[Physicsandmaths]

If you take the derivative with respect to x of xy, why isn't that simply y? Why can't you treat y as a constant?

[varsitychik0107]

thank you so much!! i'm taking a calculus test at UGA tomorrow, and this video helped alot for reviewing!!

[rust1477]

You are a gentleman and a scholar my good sir.

I'm taking Calculus at UT Austin right now, and you're making it a ton easier. Thanks and keep it up!

[patrickJMT]

glad to help!

if you see me at the FAC tutoring, come say 'howdy'!

[herinksat]

Bravo Meastro !!!!! You are very Helpfull, thanks a lot !You have been helping me a lot on my math (Calc.)

Kosovo

[patrickJMT]

glad to help!

good luck in the class!

[jrendoso]

THANKS A MILLION

I JUST DINT GET WHAT HAPPEN TO THE 3. AT THE BEGGINING THE ECUATION WAS = TO 3 AND WHAT DID YOU DO WITH IT.. ?

sorry but i din't get that

[patrickJMT]

the derivative of a constant is zero, so it 'goes away'

[lukasgomes1428]

dude you rock!

[fanfanz9]

Thank you Thank you and Thank you!!!

[hereisburo]

you did one mistake,when you differentiated y^2,it will become 2ydy/dx not 2y^2dy/dx.Isn`t it?

[patrickJMT]

yes, i have added video annotations, and there are also about 8 million comments about it

[Davoiscool]

I just don't get why when X differentiates to 1, why does y^2 not just differentiate to 2y, why does the dy/dx appear.

Same with Y without the power, why does it differentiate to dy/dx, why not 1?

[Sonolumino8939]

Because you're solving for the y term implicitly, which means that you're solving for dy/dx. Also, in the term 2y, the dy/dx appears because you are actually chain ruling it. Think of it as the differentiation of x^2. The differentiation is actually 2x * (the differentiation of x, which is 1), so 2x *1. In the y^2 problem, its 2y*(differentiation of y, which is dy/dx). Hope that helps

[DeJayHank]

You can also think of it like this:

the only difference between implicit and explicit is that the explicit equations have the "y" alone on one side of the equal mark, while the implicit don't.

when you for example take the derivative of : y= 2x+x^2 you get y'=2+2x

notice that the " y " turns into " y' " (y prime). this is because you take the derivative of both sides, and that's exactly what you do in implicit equations.

y' = dy/dx as he explains in the first example of this video

[dewi20]

thanks, really good

[rheogram]

Hi Patrick,

I am in my second year of a Maths degree. Your explanations are superb and have helped me immensely. Please keep up the good work; you bring the subject to life!

David

[howsuthen]

pratick do u know any expert site for physics i m weak in it pls give me some site for physics

[kurtpatrick100]

the derivative of y^2 is not 2y^2 dy/dx

[i1li1l]

MAN thank you soooo much...i have an exam in 3 days, and these videos are much better than (textbook + lecture notes + prof explaination)

you are the man

[patrickJMT]

ha, thanks! glad it helps

[ediota27]

thanks alot man! you helped me big time... Now i understand implicit differentiation but the test was last week and I got a fail... lol.

[patrickJMT]

just watch my videos for when u retake the class if you have to : )

[MajinBoo321]

WOW!!! ure a good teacher!!!! Thx a lot, i didnt understand this when my teacher taught me, but after watching your video NOW I DO!! TY

[patrickJMT]

good! now you will not turn me into chocolate!

[tsd5060]

I'm still a bit confused. What if they say find a tangent line , but they dont give you the y point.

Like if they say, Find a tangent line at x=1. What do you do then?

[patrickJMT]

you get the y point by plugging x=1 into the original equation and solving for y.

[porkupyne]

Thank You!!!!