Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

Some relationships cannot be represented by an explicit function. For example, x_+y_=1. Implicit differentiation helps us find dy/dx even for relationships like that. This is done using the chain _rule, and viewing y as an implicit function of x. For example, according to the chain rule, the derivative of y would be 2y_(dy/dx). Created by Sal Khan.
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[@malihareza4754]

"Let me do that in a different color..."-sal in every lessom

[@beastlybob572]

Okay, i just learned in 8 minutes what my calculus professor failed to teach in 2 hours of class time!

[@jackchen188]

same omfg

[@muhammadhamza4494]

Haha same

[@theblasters5378]

Same

[@Man-ds9ir]

Weird eh ?

[@nononomimi]

Omg same

[@mariakhan6090]

There have been a thousand maths teachers on KZbin, but nothing compares to Sal ♥️ thanks, sir

[@aamirhooda937]

Fr. He explains it so intuitively!

[@bebarshossny8405]

this channel is literally a gold mine

[@Man-ds9ir]

Bebars Hossny And 6million people have already found it

[@Man-ds9ir]

Lol

[@SadikKhan-wt8cs]

@@Man-ds9ir the best part is, that doesn't make it any less valuable.

[@Man-ds9ir]

@@SadikKhan-wt8cs Yeppppppp

[@dAvrilthebear]

Thank you, Khan! As usual, simple, clear and concise.

[@gilbertobarajas2487]

Thank you, Sal and company! This helps so much

[@gameprofile3725]

You guys are doing wonderful job . Keep it up . Love Khan academy .

[@JBMgo]

Leibniz's notation is so much easier for the Chain Rule and its applications! Try to learn implicit diferenciation using the f-prime notation and you will have a hard time.

[@sushant2664]

I am just learning, but I find Leibniz notation much more natural because of how explicit it is. It should really be only way to learn chain rule ( g'(x) • f'{g(x)} makes absolutely no sense ) and consequently implicit differentiation.

[@jeffmurphy2208]

Thank you. That makes so much sense.

[@sundayjohnson6433]

Sal is the best math teacher online that I've watched so far

[@EDUARDO12348]

This was a great example, and finally, implicit diff clicked for me.

[@xobk]

Just when I start feeling like calculus is becoming an endless series of garbled numbers and symbols, it goes and wows me again with something like this!

[@hellozukohere6514]

Literally feels like each week they add something worse. Khan academy's barely helping at this point with all these topics to keep up with.

[@brendonbalascan6814]

I didn't learn this right in calc 1 and i'm revisiting it for my calc 3 class and it's completely blowing my mind how this works. You can really just treat the derivatives as operators? that's insane.

[@noahgeorge7357]

That struck me too. If you get to upper division proof based math, you'll soon realize pretty much any operation in math is defined by an Operator i.e.(Integral, differentiation, matrix operations are all types of operators)

[@Dij21]

You make it all so simple, thank you!!! When I saw this in lecture, was scared lol

[@jimcar53]

Thanks very much. Learnt a lot

[@TomAustinIII]

Very helpful for building confidence

[@sjurhodnesdal5250]

Great video!

[@kelvinfilyk3413]

IT ALL MAKES SENSE

[@myron_jd1272]

OMG FINALLY I UNDERSTAND, ITS JUST CHAIN RULE TY!!

[@mattdabney1927]

The help text at 0:33 in the Khan Academy lesson should say (-1, 1) since he's discussing the interval over which x has multiple y values defined.

[@DiaryOfAlexPhoto]

Finally makes sense...

[@ajstordeur1857]

I love this man its 2am I'm up to doing delta math having not a single clue what implicit differentiation is and this man just saved my life for my test tomorrow. I saw that green chack on my delta math and screamed yes so loud that I'm baffled my parents didn't wake up. I love this man.

[@franklinmiranda3578]

lol congrats

[@EmpyreanLightASMR]

3:30 I think this is what i've been hunting for across the universe. In fact, I didn't even know d/dx MEANT anything other than "you're deriving with respect to x"... but you're making it sound like it's vastly more important.

[@goodgamers777]

Thank you, that makes more sense.

[@pandapanda338]

Was stuck on a problem for 2 hours now, until i found this amazing explanation As always Khan Academy to the rescue!

[@whoopsiedaisy9620]

Thankssss!! This was really helpful:-)

[@isabelamcneilly-anta5477]

omg i needed help on hw on explicit differentiation and this is the EXACT problem

[@manuelkarner8746]

4:29 "might be a little bit cleare" lol I searched 2 intense hours for exactly this chaining explanation (without knowing) THANKS !

[@jackchen188]

I love this guy

[@ryanwusmc]

Thanks.

[@ppbonner3816]

awesome video wow thanks

[@rampant6055]

This was so helpful, especially putting d/dx (y(x))^2 thank you very much. Made my life much easier

[@user-iy8lo9zw4p]

exactly i was struggling on that too

[@enkephalin07]

This contributes little to solving other differential equation, but at least it's not nothing. Breaking the terms down into separate differential operators does help clarify a novel variant of the problem, but that's not often enough.

[@katrinaWHATx10]

whoa, perfect timing! I have an exam on this tomorrow. thank you so much! I finally get it.

[@AshmitManak]

Lol, so much happened with you in these 10 years

[@wd3770]

a good explanation

[@muhammadhamza4494]

Khan academy saves me everytime from getting bad results...

[@EndermanJandy]

I failed my test on this lesson today so ima use khan now 😂

[@speedspeed121]

Sal distracting everyone with his multi color pens

[@jqyhlmnp]

I mean, now that you pointed it out :D

[@ayiboroberts7503]

Really right 🤣😂👍😉😉👍👍

[@aponmasrur8116]

in implicit differentiation why we assume y as a function of x?

[@pedrov8868]

Math is beautiful

[@afiatabassum1517]

Thank u very much sir But the derivative of that relation is not a function right? Is it another relation?

[@Lester806]

Your explained better than my textbook lol

[@zack_120]

Implicit differentiation is very weird in many cases. Doing it in this case (x^2+y^2=1) appears to be unnecessary. One just needs to rearrange it as shown at the upper right corner, y=±sqrt(1-x^2), and take the derivative as usual non-implicitly. The absolute results are the same with the advantage showing both solutions, ±x/y whereas the implicit way as shown here just gets -x/y, a half of the complete solutions. So, what is wrong here?

[@rjt1789]

Itis very nice to learn this way, thank you. However im a bit confused when it comes to terms such as 5xy2, how would i find the derivative of that with the dy/dx thing? Power rule?

[@sababatool4029]

Use the product rule

[@Delilah-qm6jl]

product rule

[@michaelcalcagni5825]

Bless

[@skyetsosie372]

I have an exam tomorrow, and literally forgot what I learned just 5 weeks ago..smh

[@Axceed1]

What does dy/dx even "mean" when when y can not be written explicitly in x? Often y will not be a single valued function of x, and if I go back to the limit definition, dy/dx will not exist because y approaches multiple values.

[@nasaman23]

the unknown derivative of a function

[@64Jro]

Look at the 3blue1brown video of implicit diff.

[@christiancostanza9952]

Crispy understanding in tangent,?

[@user-nj3qm7re5b]

I mean why we should define those things...

[@EasyFunAITraining]

Where does the (dy / dx) come from? o_o

[@FireVortex720]

Because it is a separate variable(y). Hence, dy/dx.

[@shamaranderson7755]

it's the derivative of y

[@user-iy8lo9zw4p]

thank u you r saving my engineering degree hahaha

[@technoultimategaming2999]

I don't get it Isn't d(x^2 + y^2)/dx d(x^2 + (y^2)(x^0)) 2x + 0y?!

[@arandomghost8819]

We cannot take the y out as y has some relation to x....I.e some change in x causes some change in y.....taking out y will only make sense in partial derivatives but that falls under multivariable calculus.....this is the total derivative we are talking about here

[@rifat.ahammed]

Greaaaaaaaaaaaat

[@revantthakur8495]

Sal took just 8 minutes to teach me implicit differentiation while my professor took an entire lecture.

[@qualquan]

why not use y = (1-x^2)^1/2 and then dy/dx by chain rule?

[@drofeng]

Perfectly valid. This is just a simple example of implicit differentiation

[@oblivion.4974]

What is this useful for?

[@rizwanrifaqat1399]

greetings sir! I want to study the concept of differentiation and integration right from the very basic. can u please suggest me a tutorial?

[@ellie_deli]

Rizwan Rifaqat 3Blue1Brown is a fantastic channel with a 10 part introduction to calculus series. I hardly think this is relevant 10 months later, but hey ¯\_(ツ)_/ ¯

[@Nino-eo8ey]

@@ellie_deli I wonder if its relevant 5 years later then...

[@ellie_deli]

@@Nino-eo8ey math never loses its chic

[@SF-og3fq]

I guess you could call it a relationship...

[@Zoolixify]

no audio

[@jackc.3079]

unmute

[@thevibe2316]

Isn’t this more difficult than what the the organic tutor taught? Or is it just me?

[@rosechoi7415]

Wait, I thought chain rule only applied to functions? A circle isn't a function

[@rosechoi7415]

Also why does Sal refer to y being a function of x at 4:15?

[@user-qz6zu6ir4e]

t y

[@-__-_-_--__--_-__-_____--_-___]

fucken hate watching these on the website

[@shawnthesheep2369]

lol

[@dbmuehroom8658]

WHY DOES HE SOUND LIKE RANBOO

[@abdirahmanbashirosman3433]

U are using complicated and hardway I can answer this question with 1 minute

[@buddy3387]

When is this going to help me in life??? Thanks a lot school system.

[@MrJessr0x]

hmmm maybe never, but just because you are useless to the world.