Derivatives - Quotient and Chain Rule and Simplifying

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[@ntsystem]

Oh my god. You don't know how much thankful I am. My teacher can't really teach.

[@ludwigwittgenstein6850]

For all who don't know, he cancels the 1/2 and the 2 because of the chain rule. When you have the chain rule, you multiply the power you brought down with the derivative of inside function. In this case, 1/2 x 2 = 1 or just x. You're welcome.

[@rosygyal]

I cannot begin to tell you how much you've helped me in Calculus! Teachers should just play your videos in class!

[@MangoBased]

I have a test in business calculus tomorrow and I couldn't understand combining the chain rule and product/power rules for the life of me. Now I have a chance, so thank you so much.

[@ericmontiel3234]

Thank you so much for this. Out of nowhere, my professor said we needed to simplify these for our exam....when on the HW we didn't need to. You're a life saver

[@born2race17]

In our AP Calculus class, we were taught a bit more humorous (and catchier) way of remembering the formula for the Quotient Rule. We learned it as: HoDhi-HiDho/ HoHo Where: Ho - Denominator (Ho rhymes with "low") Hi - Numerator (Hi is just..."high") Dho - Derivative of "ho" (D=Derivative) Dhi - Derivative of "hi" It just sounds a bit better that the formal way, and it's a pretty good brain trick to memorize it. It sounds pretty cool to say, as well, like a song. ^_^

[@iiheartYOUNGMIN]

OHMYGOSH I DONT KNOW HOW I CAN THANK YOU! I'm a really bad procrastinator and I have a test tomorrow. I didn't get how to simplify the derivatives, so I thought that I would fail tomorrow's test. You are a life saver! Thank you so much!!!! Thank you thank you thank you!. Omygosh the feeling you get when you finally understand how to do somehting! It's such a wonderful feeling. Thank you!

[@TriCkY4WiCkEdStYlE]

I watched the whole video without even realizing how long it was; that is the mark of a great teacher. Thanks man

[@MrElcid123]

Got a test on this tomorrow in AP calculus, actually got this in the last 5 minutes, my body is ready :)

[@patrickjmt]

@ElDirectorRJ ya, if you do not use it, you lose it! myself included; it is amazing how quickly it all goes away!

[@crimsonsky3745]

Quotient Rule: (f/g)' "low d high - high d low/ over the square of what's below" xD This another way how I learned to memorize the quotient rule theorem...a song lol the d stand for the derivative. I just wanted to share that with you! You're videos are great btw! It's been helping me through my calculus and trigonometry (:

[@patrickjmt]

yes, some girl started singing that in a calc class of mine once.. i had no idea what she was talking about : ) she just kept singing it...

[@JS-tn6tr]

10 years later this video is incredibly helpful. Have a test in under an hour and this video has done wonders. Thank you

[@foreveryoungmusic06]

Thank you for helping this lost calc student!! Much appreciation! better than the tutors at my school-.-

[@zara96100]

My life has been saved, SO HAPPY I FOUND YOU! You are a great human i love you :D - LOVEE FROM THE UK

[@punkrockzoie]

Thank you sooo much. I've been studying like crazy this week but things didn't quite click until I watched a few of your videos. I'll keep practicing!

[@LeoMessiBear10]

This video was sooo incredibly helpful, I have a test tomorrow and have always struggled with these types of problems. Thank you!

[@patrickjmt]

@SnoraxLorax you are very welcome

[@joshgc1]

You sir are the man! thank you so much, because of you i am going to graduate from University. Lots of love from Canada!

[@ubbadghani5255]

Thank you so much. I had the product, quotient, and chain rules down, but when you put them together I had no idea what to do. I have a test over this tomorrow and this has helped me understand so well.

[@patrickjmt]

well, if the discriminant is negative, it means that the quadratic will not factor into the product of two linear factors with real roots... so that is about as simplified as it would get! (using real numbers)

[@ashleydamm4967]

You just saved my life. This is by far the best video out there! Thank you!

[@laneeleanor]

Thanks you have really helped! I am open uni student and rely solely on the text book and youtube. Yor vids. Have been really helpful

[@chad8994]

I just want to thank you for your time and know how on the subject of calculus. You have helped me more than i can say, appreciate all you do :)

[@patrickjmt]

@matthooper11 no problem

[@tylerjones1773]

thank you so much, helped me study for a major exam and not many people can explain math to me easily!

[@OddFuture543]

Having trouble factoring out; this was such an easy to understand and well put together tutorial... thank you!!

[@beverlyfrancis8433]

One out of ten videos I watched addresses the inside function thing (and that's yours). Wanted to C if I was doing it right. Thanks! Old videos are great! June 2022.

[@ZhangArtification]

You are literally amazing man, I share your videos with all my fellow calculus students now :)

[@Fatherminion]

Somebody give this man a trophy.

[@rabb3306]

Been searching youtube for a video like this! Great help, thanks 👍🏻

[@ElDirectorRJ]

Thanks, goin back to ap calc this semester after a semester long break and can't remember any of this. This really helped

[@patrickjmt]

thanks calculus100, i appreciate your nice comments : )

[@DennisMski]

Thanks, Patrick. You saved my hind for algebra. You got me through trig. And now you're helping my way through physics and calculus. Great videos. I'd like to see a blackboard with neon markers... But that's just me. Hah.

[@FeVaR]

patrick your videos have helped me alot, i wanted to thank you for that

[@wonderhwu]

If you want to turn a negative exponent to a positive exponent, move it from the top to the bottom. So now it's (x^2+5)^1/2, not ^-1/2

[@clarendai3785]

YOU, my friend, ARE A LIFE SAVER OMFG even KHAN ACADEMY COUULDNT HELP ME and I stumbled upon it video and I love you thank you :)

[@ChopinSchubert]

simplify was the part that i dont know. thanks alot for the video patrick

[@RubiMercuri]

I cant believe i wasted hours asking this question on chegg and searching other stuff on google just to finally find your video and know what to do. I couldve gotten my assignment done like 5 hours ago and now i feel dumb for not finding this sooner

[@mzee101]

you are a math god thank you .... i got exam tomrrow

[@WHaAteVaA]

Thanks alot ,you saved my life , your methods are simple and easy to understand i hope you increase the amount of the examples and make them total 5 everything is perfect beside that

[@WilburRuns]

@PlasmaPrestige Yes, that's what the quotient rule does essentially.

[@calculotv1]

Buen trabajo amigo. Felicitaciones desde Venezuela. Gracias por tus aportes...

[@diff57yl3]

You Rock... i was having trouble with factoring!! You made it easy =)

[@jsmithes]

Keep doing what you do man. You really helped me a lot!

[@iAsianBeats]

Why does the 1/2 and the 2x cancel out again ?

[@patrickjmt]

happy to help!!

[@andym1508]

thank you so much, so happy i came across ur videos you explain it so much better than my useless teacher :D

[@patrickjmt]

@mason0444 no, i am patrickjmt

[@wimbledon5353]

Thank you so much patrickJMT for simplifying this very unsimple part of finding derivatives...:)

[@vinoddrupali6117]

you explain very well. now i really understand to factor things out

[@dtbjjrb]

You are awesome. In the future, I may thank you for all your videos, depending on how many I watch :P

[@KieranD5896]

You have literally just saved my life.

[@prajmenon9]

The simplifying made so much sense, thank you!

[@rabillst2551]

omg u r awsom...thx alot ...my instructor needs ur tuition:)

[@jerrywebster7678]

Patrick , I'm curious about your view on why so many students claim to not be able to grasp what is taught in the classroom. Surely most math teachers are quite good at explaining.

[@patrickjmt]

thanks gellyb!

[@dorisgarzon128]

this is the greatest explanation ever!! THANK YOU

[@Robbery1211]

There was a part in here where you simplified the fractions. I do not know if that is the exact name for it. But I am referring to the part where you simplified an equation to the third power from an equation to the fourth power and added the equation to the fourth power again. If you watch your video again, (I am talking about the part where the time is at 3:32). Can you explain this a little further. I am lost.

[@58fubu]

thank you so much man...you really helped me out big time...

[@gellybelly2]

Thanks Patrick. Another great derivative problem. :)

[@rynoweston]

Thanks for doing this beast problem. It was a good review for my test next week. You're the man.

[@xghoulxx]

@chupakabra you can just do this: square the bottom. take the product rule with a minus sign on top and then multiply times a negative sign. it would be like -(f g'-g f')

[@bigMtotheL123]

Love you man! Can't wait to kill it at the exams tomorrow

[@kellygarcia4508]

Great job, it really did help. Good job at explaining. Totally will check your website 👍🏼

[@patrickjmt]

u said it

[@Mr587326]

You helped me soooooooooooooooooo much. Thank you!

[@EdwardWongHauPepeluTivrusky-IV]

This is exactly what I needed. Thank you

[@MathMikie]

it doesn't simplify you said it doesn't because b^2_4ac is negative which means the roots will be complex but can it still simplify even if the roots are complex

[@SM-qn7sr]

I get the moving the terms with negative exponents down part. But how would you simplify something like x^-1/2 + y^-1/2 divided by x^1/2 + y^1/2? I can’t just move the numerator down because it’s 2 terms. How would I be able to simplify something like this?

[@xstncd]

Thanks Alot! You > My Teacher!

[@matthooper11]

legend.....thank you patrick

[@tonymurphy6952]

your 35 minute video on 25 differetiation examples is no longer available in Ireland or so youtube tells me. can you fix this please Patrick , thanks man

[@MueedVI]

Why simplifying is needed when the total marks for a question is only 1 or 2? Just derivate the thing and be done with it. It may be needed in real life but not in exams.

[@matthewmiclat2733]

You have explained better then my professor , while your were explaining i know that you know what you're doing , unlike my proff i can see through her that shes getting rekt by teaching

[@virgilorlydelapena6942]

Please help me, how did he factor at 3:30. I don't understand what he did. Please someone help me. Got a quiz tomorrow on this.

[@kunalgupta9263]

he just took out the smaller power that was -1/2 and then inside the bracket he left( x^2+5 )^1 soo that ....1 + (-1/2) = 1/2 ...that will give the same result soo even after taking out the different exponent -1/2 we will get the same result that was 1/2 hope u understnd wht i was trying to clarify here all the best cheers:)

[@patrickjmt]

keep trying : ) it is tricky at first!

[@JoshuaTaylor1992]

I like using "lodhi minus hidlo over lo squared :) helps me memorize quotient rule so much more easily. sounds like a song :P

[@SnoraxLorax]

This was sooo helpful. Thank you!!

[@timsoll]

Thank you. You just saved my life!

[@chupakabra]

Isn't it possible to just use the product rule for division instend of having to remember two formulas or working with the trickier quotient rule. I think I read somewhere about that but I can't remember where.

[@nedzadish]

Can we use just chain rule instead of quotient rule, to write (x2 + 5)-1/2 in the nominator instead of writing (...)1/2 in denominator position?

[@biodancer522]

You're a life saver!

[@trez134]

Thank you so much! This is extremely helpful.

[@asteria8291]

Thank u very much, even though ur vid is 10 years old but its still serves good! U helped us alot thanks!

[@Syruscleat]

Very refreshing Dude.

[@dutchiplays]

YOU'RE THE BEST! Thank you for helping me. Thank you :)

[@lorenzkristineliu6392]

coooooool. :> i easily got over it. i thought chain rule was difficult. thanks. :3

[@killer99520]

And again you helped me. thanks

[@Bbriamalupa]

Why gx² , 1/2 is cancelled?

[@kevindose1431]

At 02:34 he said the 1/2 x 2 make it disappear. Now when he rewrite the clean equation, the 1/2 that was attached to the (x2+5) disappeared somehow... Anyone????

[@BandytaCzasu]

It cancelled out with the 2 on the racist... I mean far right.

[@yz249]

Watch past it, he adds back the ^1/2 10 seconds later.

[@TheRedParallel]

Can you please explain more on how you simplify and factorise.. i don't get how 1/2 cancels out 2x etc and why you pull out the x... can you say why you do instead of just doing it. thanks

[@SM-qn7sr]

What is 1/2 * 2? It’s 2/2. What is 2/2?

[@TheYummypeaches]

helped me a lot thanks!

[@Minerva578]

Hi, i was just wondering. What if we move the denominator instead having the numerator goes down. I did this, so am i correct or nah? Just like at 5:03 nut revrese instead the denominator goes up plus i uses product rule sk there's no denominator as if is implified the function

[@mazhar3447]

thanks man really helpful

[@6727bluejays]

Thanks a lot, you help me more than my tutor that I pay good money lol.

[@marcyjohck1077]

what happens if you have 7/(3x^2-4)^4 does the seven cancel out as a constant?

[@mana6945]

Low D High minus High D low Square the bottom and Here we go...

[@PatsPTL]

Thank you so much!

[@1227mimosa]

You are amazing, thanks a lot for helping me :D