Simple trick for doing implicit differentiation!

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[@nact8917]

SAVED MY LIFE!!! I have a midterm Wednesday and could not understand this stuff for the life of me!

[@actual.education]

😊 Awww I appreciate that! Good luck with your midterm!!! ✨🤞✨

[@ogunnaikesegun5949]

Thank you so much bro. You just save my grade

[@actual.education]

You're VERY welcome! Happy to hear that :)

[@ryanlane6268]

swear every 30 sec video i find on this bs is worth 30 hrs of my own time studying ty 🖤

[@actual.education]

Glad it could help!

[@rommelbartolome6452]

You taught something that a professor spends hours in 30 seconds

[@actual.education]

Time is money 🤑!

[@kaveetwins]

Thanks so much my man 🔥 . This method is quicker than we thought .

[@actual.education]

Awesome to hear! Yeah I was always confused with the usual method they teach this.

[@madingthree]

Implicit differentiation/related rates: when you learn that dy/dx is technically just a fraction that is also not a fraction

[@actual.education]

haha, yeah calling things an "operator" tends to scare people off at first, working it like a fraction works for the most part and is way more familiar to intro students.

[@sushitootie]

thank you so much sir for this wonderful technique, it's very concise and very helpful for us students. I'm very glad to learn this, since it'll be my midterm exam tomorrow. 🙌🏻

[@actual.education]

Glad it could help you out! Good luck 🤞 on your exam tomorrow!!

[@AyomideAyodele-qj7bg]

I love love this. All the way from Nigeria

[@actual.education]

@@AyomideAyodele-qj7bg love that we can help out from different continents, thanks 🙏✨

[@saathvikbogam]

There's a simple formula for this, dy/dx= -(∂f/∂x)/(∂f/∂y) where f(x,y)=c is a implicit function in x and y and ∂f/∂x is the partial derivative.

[@actual.education]

Curious where the negative comes from? May be a cool trick but I'm pretty sure all those partials would scare off students who already struggled learning it the standard way.

[@saathvikbogam]

Let's use your example for this. f(x,y) = 4x⁵ - 6y⁴ + 2x² - 2y = 3 Now according to your method, we take the derivative and multiply each component with dx or dy. 20x⁴dx - 24y³dy + 4xdx - 2dy = 0 (20x⁴+4x)dx + (-24y³-2)dy = 0 Notice that the coefficient of the dx term is the partial of f with x and coefficient of dy is the partial of f with y. (∂f/∂x)dx + (∂f/∂y)dy = 0 (∂f/∂y)dy = -(∂f/∂x)dx dy/dx = -(∂f/∂x)/(∂f/∂y)

[@actual.education]

@@saathvikbogam oh very cool! I see the negative now, thanks for the clarification ✨🙏✨

[@sanjitkumarmandi465]

Thank you so much

[@actual.education]

You're very welcome!!

[@Chancethecapper]

I just learned my teacher’s hour and a half lesson in less than 3 minutes

[@actual.education]

ah yes, the power of memes

[@bunmarceno5673]

my man is a fuckin messiah. thank you.

[@actual.education]

Gotchu bro ✨🙏✨

[@debrucey]

So y’ = dy/dx?

[@actual.education]

Usually yep!

[@sttlok]

"divide both sides by dx" I died

[@actual.education]

Don't unalive yourself yet 🙃

[@jvbassin2391]

It helps if you write every dy or dx in respect to dx as you go so you don’t need to do that division stuff at the end👍

[@actual.education]

@@jvbassin2391 sure, but then when students also have to also remember which one they derived when doing a product rule, just always doing a dy or dx makes for less mistakes

[@shivanshnigam4015]

-(partial derivative of f(x,y) wrt x)/(partial derivative of f(x,y) wrt y)

[@actual.education]

Yep! Some people just don't get partials at this point in calculus class (it's more a vector calc concept)

[@Jabari10]

Bro thank you

[@actual.education]

@@Jabari10 gotchu fam ✨👏✨

[@sharkwatcher305]

for this video to show up while studying final calculus it's hella useful 👍👍

[@actual.education]

Glad it was useful! Feel free to join our discord/twitch if you wanna ask more questions and get free help!

[@Fr3doskin]

They're not explicit about it 🌚🌚🌚🌚🌚😂

[@actual.education]

always here with the Dad jokes

[@Atharv-bo4uz]

Thanks sir 🇮🇳❤🙏

[@actual.education]

You're welcome beta ✨👍

[@zabi1185]

can u use this method when dealing with higher order implicit differentation?

[@actual.education]

It gets weirder for doing second derivatives - I'll make a video on it soon 👍✨

[@neilvincent]

There is a much quicker method from partial derivative.

[@actual.education]

Sure! This is just a way to understand without having to know partials

[@tusharaggarwal1412]

@neilvincent hey bro I've been trying to understand the logic behind implicit for a while can you help me

[@neilvincent]

@@tusharaggarwal1412 i also dont know the logic i just know the formula my sir told me that in higher mathematics we will know the logic behind the formula

[@tusharaggarwal1412]

Oh ok , so it'll not be that complex if I learn partial differentiation?

[@neilvincent]

@@tusharaggarwal1412 yes

[@jijumon3443]

Thank you sir

[@actual.education]

you're very welcome!

[@basil9633]

W

[@actual.education]

Beeeeeeg W

[@Hope_Maphosa]

Thank you

[@KookyPiranha]

we deriving conic sections with this one 🔥🔥🔥

[@actual.education]

oh that's cool! haven't seen conics derived that way before, usually it's the two cones getting intersected by a plane

[@baldaiomir]

Easy way? That’s like the main method for finding dy/dx

[@actual.education]

the usual method I see taught is to take the derivative of everything with respect to x and then dx/dx = 1

[@smfarooqnaqvi99]

DY/DX= (10X^4 + 2X)/(12Y^3 + 1)

[@abiodunshittu8402]

You can different as -(different only the x variables)/(different only the y variables)

[@actual.education]

yep that works as well!

[@Yashbansal1511]

Thanks very much it helped me a lotttt....👍😊

[@actual.education]

Most welcome 😊

[@teenage_socialist_edgelord]

Or just apply the chain rule to the ys only and solve for dy/dx

[@actual.education]

Sure that works too, just get confusing when doing product rules

[@triple_gem_shining]

I dont see how this is "easier"

[@actual.education]

@@triple_gem_shining idk, I mean if you read the comments there are a few people who found it easier 👀

[@lolislayer1643]

So just take the partial derivative of y and divide by the partial derivative of x?

[@actual.education]

As long as you do the derivatives of both X and Y this will work

[@TMEMORIES.]

Simple

[@tommyliu7020]

Can you do a implicit differentiation video for f(x, y) as well? And also show more terms that are mixed? Like x*Ln(xyz)

[@actual.education]

Good ideas for another video! If you need help quicker feel free to come by the livestreams and I'll demonstrate it

[@darewolf_7419]

Thank you very x10^200000 much for doing this, now i can sleep well

[@actual.education]

That's a whole lot of 0s 😅

[@darewolf_7419]

@@actual.education You deserve it!!!! 🫡🫡

[@العهدالجديد-ن9خ]

Why you attach dx to x expessions I thought you only attach dy/dx to y expression?

[@actual.education]

That's another way to do it - attaching dy/dx to only y expressions and multiplying all the way through by dx gets the same result.

[@Tommy-jq2ju]

Can you do this with a term that has both x and y in it or is this rule only for single terms that are isolated

[@actual.education]

Then you do the product rule. So for example x²y³ would be (2x)(y³)dx + (3y²)(x²)(dy)

[@Tommy-jq2ju]

This is a much easier way of doing implicit, why don't most professors teach it this way!!

[@actual.education]

@@Tommy-jq2ju ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯

[@uwugang6985]

Hi i need some help on this: (y - 0)^2 = -533.4(x - 1500)

[@actual.education]

Do you need to find the derivative of it?

[@darcash1738]

To anyone struggling with implicit differentiation, learn feynman's technique and exact differential equations. The idea of y having a derivative in its own respect is very similar Note: it is similar because it is negative partial derivative in respect to x/ partial derivative in respect to y. Since x is a constant in the "y world", its derivative is 0 there. Since y is constant in the "x world", its derivative is 0 there. -[∂/dx(4x^5+2x^2)]/[∂/dy(-6y^4-2y)]

[@actual.education]

This is cool! Feynman was a G ✨👌

[@darcash1738]

@@actual.education Absolute legend for real. Im trying to get better at being able to do his technique. Sometimes it ended up with things like f(a) = f''(a) so I also had to learn a bit of differential equations 😂

[@tusharaggarwal1412]

​@@darcash1738 hey bro I've been trying to understand the logic behind implicit for a while can you help me

[@darcash1738]

@@tusharaggarwal1412​​⁠​⁠yeah totally man. I’ll explain it in general and then with partial derivatives which makes it quicker. In general, you’re going for dy/dx, also written as y’ sometimes bc it’s clear we’re getting the derivative in resp to x. What does that mean? Change in y for an infinitesimal change in x. So when we take derivative in respect to x, dx/dx is just how much x changes/a change in x which is ofc just 1 so we ignore it. We know everything else from power and chain rule. Let’s just say “m” is the power of the term in question for x’s and “n” for y’s. Everything pure x is just mx^(m-1). Anything pure y will be ny^(n-1) dy/dx. Something like x^m*y^n will use chain rule. mx^(m-1)y^n + ny^(n-1)dy/dx * x^m. Then, algebra to isolate y’(dy/dx)… All terms without it go to the other side. Make the left side y’*(terms with y’). Then divide the terms that you factored out y’ from to the other side, getting your result. Doing the partial derivative way, get it in the form of (X and/or Y terms) = Constant Then do -[Dx/Dy]. By D(var) I mean partial derivative in respect to that variable. A partial derivative means you do the derivative while treating all other variables as constants. Eg, constants derivating being zero rule: - Dy(x^m) = 0, - Dx(y^n) = 0, And constant multiplication rule: - Dy(y^n * x^m) = ny^(n-1) * x^m - Dx(x^m * y^n) = mx^(m-1) * y^n Eg: Dx(4x^2 + 8xy^2 + x^3y^9 + y^8) = (8x + 8y^2 + 3x^2y^9 + 0) TLDR: If you understand how partial derivative works (just treat other variables as constants)… Get in form of (Terms w/ x and/or y terms) = const, Your Answer = -[Dx/Dy]. By Dx and Dy I mean partial derivative in respect to that variable.

[@tusharaggarwal1412]

@@darcash1738 thanks a lot brother , can you tell me how're you learning differentiation and partial , college or any channel on yt or any books? if possible can you share the name , thanks a lot again

[@josiahsmith9657]

Okay cool But please take out a factor of -1 and cancel is that’s driving me nuts

[@actual.education]

Don't focus on the negatives in lyfe 🙂

[@vortexfitness44]

Dude that’s insane, thanks

[@actual.education]

Yw bruh 💪

[@forthehomies7043]

Nice example

[@actual.education]

thanks!

[@samuraijack8255]

Damn bro, thank you so much!

[@actual.education]

sheeeeeeeeeeeeesh you're very welcome!

[@generaldream6206]

thanks this makes it look ez now my teacher just confused me on this. I got an exam in like under 2 hours rip

[@actual.education]

glad it helped! good luck with your exam ✨🙏✨🙏✨

[@danielshin4515]

god bless your kind soul sir

[@actual.education]

Appreciate!!

[@emalali9447]

It's so easy. Why was this ever hard to me at first?

[@actual.education]

Sometimes the way teachers explain it is confusing, also they probably didn't have as many memes 😅

[@OreoPc]

What if both x and y are present?

[@actual.education]

Then you do the product rule. So for example x²y³ would be (2x)(y³)dx + (3y²)(x²)(dy)

[@alphareturns2829]

Nicee

[@actual.education]

Thanks! Hope it was helpful!!!

[@pjb1756]

Well this is so much easier! Tnx

[@actual.education]

Glad it helped!

[@axillaryroulis460]

Thank you so much. This video is a literal grade saver for me❤

[@actual.education]

You're very welcome! Good luck with your exams 🤞✨

[@Jesus_Nevarez]

Theres an easier way than this

[@actual.education]

easier is the eye of the beholder

[@0bleach0]

Smart

[@thomasshelby-be3kh]

What to do when it's given (x^2y or xy^2)

[@thomasshelby-be3kh]

x^2.y or x.y^2

[@actual.education]

@@thomasshelby-be3kh just use the product rule. So x²y -> 2xy dx + 1x² dy

[@brandenlopez7407]

Wrong

[@actual.education]

sometimes you don't want to be right

[@NadergeLouis]

Is that high school 0-0

[@actual.education]

It can be if you take AP calc

[@mrlordsaif5708]

You could also just use partial differentiation

[@actual.education]

yep! but sometimes that confuses people

[@ComputerJunkie]

i think what he’s doing is contrived from the partial derivatives identity, just in a round about way, if you have dy/dx= -partialx/partialy cross multiply and move everything to one side you end up with what’s on the second line edit: forgot negative

[@actual.education]

@@ComputerJunkie exactly. It makes more sense when you have chain rule/product rule type stuff and can't keep track of what variable you're driving with respect to

[@domdom-hh9tx]

WHERE WERE U BEFORE MY MIDTERM EXAM UGHHH

[@actual.education]

Probably eating breakfast (it's my love language), but I have a lot of other calc videos that you can check out for help with your future midterms!

[@domdom-hh9tx]

@@actual.education noted sir, thank you!!! we're in antiderivatives now, im hoping i pass the 3rd exam :3

[@johnnosa]

Awesome !!! Useful 🥺🙌

[@actual.education]

Glad it helped!

[@mercifulshehz1656]

Thanks a lot for this method ❤️

[@actual.education]

Happy to help!

[@sarahcaglayan5808]

THANK YOU

[@actual.education]

You're very welcome 🤗

[@isabellacartas9328]

You are such a king

[@actual.education]

Thank you!! ✨🤴✨

[@joshreveche4501]

thanks bruh

[@actual.education]

Gotchuuuu

[@bluet.]

whoa whoa

[@bluet.]

ngl, I understand the basics of this. but it gets confusing when the product rule and stuffs like sin and cos is involved 💀

[@actual.education]

Yeah those can't get tricky especially if there's also a chain rule involved, the important thing is to take it step by step and try to keep track of where in the chain you are

[@techhub_]

Thanks man

[@actual.education]

You're welcome! Glad it helped ✨🙏✨

[@yungmaz13]

What if you had a product of x and y?

[@actual.education]

You would use the product rule. So for xy it becomes y•dx + x•dy

[@yungmaz13]

@@actual.education Thanksss

[@adityamishra0706]

Use partial differential bro

[@actual.education]

Can't use it if you haven't learned it yet - partials usually come up in calc 3, but brool story co

[@adityamishra0706]

@@actual.education but I know

[@actual.education]

@@adityamishra0706 that's great, then use it. This video is more for calc 1 students who haven't gotten that far yet.

[@adityamishra0706]

@@actual.education actually I'm a grade 12th student. Not even in college

[@boxlad7583]

how is this a trick lol, this is just a different and equally long method that I've learned in class

[@actual.education]

Tricks don't necessarily have to be "quicker", but if you read the other comments for some students it's definitely "simpler" (to them) than the method you usually learn in school

[@generaldream6206]

idk man this seems 10x simpler and 3-4x quicker than what my teacher taught

[@boxlad7583]

@@generaldream6206 been out of calc for a while now so I forgot all this anyways lol. if it works for you that's all that rlly matters, good luck out there

[@IsabelDelgado]

Gracias friend

[@actual.education]

de nada :)

[@AmCanTech]

Doesn't that 2 disappear because its a constant ?

[@actual.education]

if you're doing it this way, there's still a dy attached to it

[@lockk405]

Find Y ima just draw and arrow to it and tell my professor there it is found it.

[@actual.education]

Haha, hopefully you at least get some partial credit

[@adrianedavid2298]

How about if the given has xy?

[@actual.education]

this would require you to do the product rule, so it would be (xy) -> x dy + y dx !

[@daniellongoria405]

This is so great thank you so much. I have a calc frq tomorrow.

[@actual.education]

you're very welcome! good luck with the frq! ✨🙏✨

[@Vishnu-jr3wv]

Bro why ee taking dy and dx after the function

[@actual.education]

It's a trick

[@tinytidbits]

Thank you great video keep it up

[@actual.education]

Thanks, will do!

[@aidanonbrawl7287]

It’s easier to just find the derivative with respect to x (d/dx) so when you differentiate a variable you get dy/dx instead of writing dx for x and dy for y. Makes it much simpler to look at

[@actual.education]

sure, but then when students also have to also remember which one they derived when doing a product rule, just always doing a dy or dx makes for less mistakes

[@aidanonbrawl7287]

@@actual.education nah I’m taking BC and i haven’t encountered anything other than f’(x) or y i rlly don’t think that’s necessary

[@actual.education]

​@@aidanonbrawl7287oh just wait till you get to related rates then 🤯

[@danbocker7398]

Bro this way takes much more work. Just add dy/dx after taking derivative of y

[@actual.education]

And what about taking a derivative of x? 👀👀👀👀

[@kingkevster613]

you dont have to be taking dx for every x you see because dx/dx = 1 so you would leave it as is, and can save time@@actual.education

[@ebhojayejuliet9728]

this is not an implicit function

[@actual.education]

But it is implicit differentiation

[@justinsmith1053]

This is so much better than trying to remember to multiply terms with y, by y prime. Thanks a lot sir!

[@actual.education]

You're very welcome!!

[@aumvishwakarma5215]

As a jee aspirant this is just a piece of cake

[@actual.education]

I thought the cake was a lie

[@BidensHusband]

Dividing by dx is a whole new level of messed up 💀💀💀

[@actual.education]

But it works ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯