Implicit Differentiation (part 2)

A hairier implicit differentiation problem.

[@18nabeel]

7 people either hate math, or they're some random money charging math tutor

[@turmoil9]

hilarious

[@prathameshsawant5574]

now 13

[@jackchen188]

18

[@archilzhvania6242]

or maybe they don't like the turtle pace of learning.

[@alialtan129]

36

[@dozza92]

lol, penmanship!

[@manfrommars340]

well arent you a superstar

[@dcs_0]

Does 10 hour course on brilliant: Kinda understands implicit differentiation but not really Watches 10 minute Khan academy video: 100% understood :)

[@diegosolis5545]

Watching this video has helped me understand this more than sitting in class

[@Washedsortof]

I was so proud of myself. Lol I actually was able to do this by myself

[@Fhlaejin]

i come to these videos every single time i have class, and watch them instead of trying to understand my genius professor. You have helped so much, thanks for the awesome videos :)

[@mygeeknation]

You are the sexiest Charles I've ever laid eyes upon

[@vilaskadival]

Animated calculators ain't geniuses.... They are just weird.... Not even human, heck, not even completely an organism.

[@theorist353]

Hey cussandra, you grew up

[@silverstar305]

THANK YOU SOO MUCH. I have hope now :)

[@seggyRK]

Fun stuff, Im taking Cal 1 right now and I'm getting ahead just learning from your videos. Good job Khan, you and your team deserve Nobel prizes in my opinion!

[@reve9552]

Khan Academy deserves some medals

[@zeeiggy]

thanx, im actually starting 2 enjoy maths again because of you :)

[@hemiacetal1331]

9 year old video

[@lulp07]

which program you use?

[@prestongraham3936]

why is the derivative operator placed after every y term?

[@ultimakey3111]

Preston Graham I think it’s because y depends on x and itself while x just relies on itself

[@ectoplasm12345]

its because you're taking the derivative of y with respect to x. At the end, you want the dy/dx term there so you can rearrange to get it. The other reason is because d/dx = d/dy * dy/dx because the ys cancel like multiplying fractions. Its like in rationalising the denominator of a fraction, or the chain rule. You put the d/dy instead of d/dx so you can do calculus to it, and the dy/dx is just there to "correct back" to what it was originally.

[@kumarsatyam1604]

hey sal, nice explanation. use of less bold and more clear pen will be appreciated

[@bsivoljr]

Talk about a Dream within a Dream...Within a Dream

[@totasalam7060]

best teacher ever thank you soo much

[@fmp000]

Thank you very much. Extremely helpful!

[@Cherryxx101]

where is the video that has y=x^x

[@jacobdhd]

implicit differentiation part 1

[@tylerj26]

This is almost exactly like two problems in my book that I've been struggling with. Perfect example. Thank you so much!

[@khanacademy]

That is correct

[@WOLFNBEAST]

very helpful, I have my Calculus I exam and three hours and I'm learning more than I did in the class

[@ruaraidh74]

Holy crap I've been here for hours and you just solved all my problems in 10 minutes

[@viktorolsson5927]

I thought it looked as it would simplify to: y, oh god no, dear god y

[@shaashwatkale1330]

I Didn't understand why derivative of y^3 can't be taken as 3y^2 straight away

[@curtisjb1983]

I am very impressed. You put up all these videos, yet you are still able to pay attention to the comments and respond when necessary. You are doing a great job my friend.

[@insert_a_good_name_here4585]

“If you understood how to do that, you understand how to do implicit differentiation”. I know that hardly anyone will see this, but after watching Mr. Khan’s first vid on this (and no prior experience) I did this problem before watching the solution. A testament to how thoughtfully constructed and well-put his videos are that even I was able to do this after just one thorough explanation (vid one).

[@rabitamang9746]

2²zz

[@xanaphuis]

So when Sal did the chain rule for the cosxy part... did he use the product rule within the chain rule?

[@architbhonsle7356]

Yes

[@architbhonsle7356]

That was a really fast reply wasn't it

[@yourmom7777]

hey, btw i love your videos. its a lot of help. but i wanted to ask if you could do some related rates problems, such as: Abeacon that makes one revolution every 10 s is located on a ship anchored 4 kilometers from a straight shoreline. How fast is the beam of light moving along the shoreline when it makes a 45 degrees angle with the shore? thanks, nathan w.

[@isreasontaboo]

This used to confuse me a lot too until I realised it's just that dy/dx is tacked after an application of the chainrule where, because you do not know the inner function explicitly, you literally write dy/dx instead of deriving it at that point. Dunno if that was clear or even more confusing? It might help to just spell it out loud that you want to derive blob, don't know what blob is so literally write blob' or d/dx (blob) at that point and it's the later solving for dy/dx that will in fact re

[@Seedofwinter]

I know what a derivative is; I got the concept. What just nettles me is this concept of "the derivative of y in respect to x". What exactly does that mean? I thought that a derivative is a slope of the tangent line regardless. This has really been confusing me.

[@enjoyablesounds]

Other example is the notation sin^2 x ( meaning sinx . sinx) Why is this..again confusing. just write (sin x)^ 2...sorry i am just getting into heavy calculus and i am frustrated knowing things could be explained much more straight forward. Sal you are great and I love your videos. Greetings from Delft

[@RESTNPEACExX586]

I watched the video and i really thought i understand but when i did my homework my answers still aren't correct. could you please do my question. Find the slope of the line tangent to the graph of 4y^2-xy=3 at the point (-1, 3/4). Somehow the answer is 3/28.

[@danielkim5477]

Hi you did this and i kinda understand why you did this and distributed the -sinxy: -sinxy[y+dy/dx(x)] =-ysinxy+sinxy(dy/dx)(x) But would it be incorrect do this instead: -sinxy[y+dy/dx(x)] =-sinxy^2-sinxy(dy/dx)(x) It just seems simpler this way

[@salimhuerta2699]

I have been sick for a week and have had vacation for a week and am now going to come back and I seriously thought this was very easy hopefully it translates to my calc test I'll have to make up some time this week.

[@abilashvarghese4108]

Thank you dad

[@panchomarin]

watch the first video or google the following " larson calculus pdf" around the page 152 ...at least in the spanish version... derivatives are explained in a simple practical way

[@crazybro4294]

What does "with respect to x" mean? I don't see the distinction between the variables x and y and I seem to have missed the definition of that term a while ago and now I'm very confused.

[@yermomrhot]

lol.. oh yeah product rule.. this topic is hard but fun to solve just like trigonometry's proving.. unlike that integration by parts.. oh well exam just passed.. thnks bdw

[@needsmorsleep]

It's chain rule, so the derivative of the outside is 3y^2 and the derivative of the inside is dy/dx; if you don't get why Y becomes dy/dx rewatch the last video. GL!

[@brandonogden3498]

I must be the dumb kid in class because I'm still lost. Is the dy/dx an operator or an actual fraction, and from whence does it appear from the d/dx??

[@vibha9590]

@Brandon Ogden, d/dx is an operator and it signifies the rate of change in the function lets say y WITH RESPECT TO x and not divided by x , nor does it represent a fraction of some sort. the dy /dx implies rate of change in y with respect to rate of change in x OR delta y / delta x Although, i am pretty sure you know that by now cus its been a yr since your comment ://

[@bfm987]

the 3 people that hit clicked on the dislike button probably thought it say DIS-I-LIKE....oh thanks by the way for the vid haha helping me get through 1st year uni

[@SphereMaster001]

When he did the product rule at around 7:00, why is the derivative of y always dy/dx but the derivative of x isn't dx?

[@enjoyablesounds]

and i lose you at 1:59,,sigh.. i cannot grasp the saying "with respect to" ...how come you use the chainrule here.

[@TheSweebster]

How come there is dy/dx next to certain parts of the equation? Is that to note that those are the derivatives of the original parts of the equation? I've yet to take a calc class and am trying to prepare somewhat for whats to come.

[@jannes3290]

It's because of the chainrule, understand the chainrule and you'll understand this video

[@BostonRoger]

@Madawc you usually dont get just an x, usually problems will give you a point (x,y) and you can plug that in.

[@Nyixta]

What if I have to get the value of dy/dx when x = 0? What happens to the y's since they are all unknown?

[@banifacio]

You could, but you'd need to use the chain rule first. The xy is part of the angle measure.

[@Teivel666]

for the (xy^2)...isn't the product rule: "a" times "b" prime plus "b" times "a" prime?

[@jacobwestbrook9527]

Im getting ready for calc 3 afyer 5 years, and that first problem (xy2 and cos(xy)) was really giving me a headache, I'm so glad I found this video, appreciate all you do good man

[@coronapalaciosmiguel8179]

why you didnt use the derivate rule U*V U=cos x and V=y ?

[@scurty2]

@supercalifragilismic It's cos(xy), he just didn't have the brackets around the xy.

[@lizn8412]

God bless your kind soul :')

[@forfreedom61]

The final answer seems awfully complex. Could it be simplified in any way?

[@Zilloh]

Is it too weird that I'm watching this as a hobby while painting my nails?

[@alitou001]

@AkimotoMichiyo1428 watch the videos of derrivatives and you will get it.

[@enjoyablesounds]

please don't tell me it's because we'd like to disregard the parentesis.

[@yermomrhot]

can anyone help me? i dont actually get it on how you do d/dx (xy) :S

[@Emily-en8rt]

how do you know when you're supposed to do y' and not x'? Like why when you take the derivative of y you do y' but when taking the derivative of x it's not x'? how do you know?

[@erickjoshuanebreja6154]

Emily its denominator is your clue, the d/dx or d/dy. It could be anything

[@ErcleeIsBoss]

i dont get which terms to put dy/dx next to. someone please explain

[@shantinim6834]

why is no one talking about how hot his voice is😧

[@gotmysentra]

Is it possible for you to do a problem similar to x^2+5XY+Y^2=5 ?

[@elizabeth1703]

At first I was wary... but by the end of it, I can really appreciate its unapparent simplicity. It is a messy way of finding a derivative. As of yet, I'm not aware of other benefits of implicit differentiation than taking a derivative of a relation as well as a function. I'm sure further into my course or another course, I will see what it is for.

[@Infinitesap]

Not a good Press ration. The instructor seems confuced!

[@MegaZambam]

thanks a lot, very helpful. better than my textbook

[@tuna34joseph]

ı do not need to struggle to understand my lecture in university. These videos teach me wahtever ı do not know and help me to understand my lecture whenever ı am confused.

[@michaelfred8952]

Life saver!

[@fargoth7]

I wanna see day9 do these, I would so watch them

[@AkimotoMichiyo]

Can someone explain why the y^3 became 3y^2(dy/dx) , where did the dy/dx come from, the alst video he didnt have dy/dx, only d/dx (1:50)

[@shubhmittal1189]

AkimotoMichiyo1428 here according to chain rule First we took the derivative of y3 with respect to x that is dy/dx Second we took the derivative of y3 with respect to y which is 3y2

[@pspabiel9]

couldnt you use the product rule for cos xy?

[@subcmdt]

Sal is the man, Sal for PRESIDENT!!!!

[@avelamanqina3169]

hi_wats the derivative of y=tan-1x?

[@BandofCandS]

Thanks, you helped me sooooo much.

[@lester8430]

It's always appreciated, Mister Khan. Thank you for all your work.

[@piusdarko5581]

pls solve cscxy=xy for me

[@yoooGmoney]

thanks Sal you are the best :).

[@Capt_Dango]

my head has just exploded....

[@isreasontaboo]

That will in fact reveal it.

[@81johnnyk]

Implicit d'French iation

[@erickjoshuanebreja6154]

I have a question: if every polynomial function has a dy/dx, since dy/dx will be factored out, does that mean its derivative is zero????

[@swagotosurjodutta7341]

Erick Joshua Nebreja, derivative is 0 only when the term has a coefficient of (x or y)^0.

[@gregg4]

It is. And he did that.

[@sadhikkommaddi5202]

hello sir , can you tell me the methods and procedure to slove implict equations

[@heat3]

thank u so much!!!!!

[@KimGib15]

OMG!!! im having so much trouble in my calculus class here in college.....but after watching ur video i truely understand....THANKS so much for this tutorial....ur so helpful....thanks again!!!

[@kleenextoiletrolls]

Sal are you single?

[@shiv86]

ahhh awesome sal !

[@zortog1]

that was beautiful

[@Tonykiprop]

Thanks a lot man.

[@curtisjb1983]

Very impressive!

[@Cheiiba]

You're the man!

[@benusherr]

wow. awesome.

[@hassan091289]

too confused

[@DrQlimakz]

funcception

[@Infinitesap]

Presentation

[@NinjaEry507]

Im always amazed of how you figure out stuff like this im like WHAT! at first but then you come along and everything is all clear to me ... thank you :D

[@SuperAbc2015]

Thanks That's helpful Make more examples about it

[@utsawin09]

*claps*

[@enjoyablesounds]

1:50 sorry

[@blok31092]

excellent video, took a difficult concept and made it easy to understand!

[@shyfulwahid9973]

nice