# Quotient Rule Made Easier (NancyPi)

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Published on September 23, 2018 by

MIT grad shows an easy way to use the Quotient Rule to differentiate rational functions and a shortcut to remember the formula. The calculus Quotient Rule derivative rule is one of the derivative rules for differentiation. It's used to take the derivative of a rational function. To skip ahead: 1) For an easy way to remember the Quotient Rule formula, skip to time 0:21. 2) For an example of how to use the Quotient Rule to take the derivative of a fraction or quotient of functions (rational function), skip to 1:41. This video is a basic introduction to the Quotient Rule for taking derivatives in calculus. Nancy formerly of MathBFF explains the steps.

For more help with Quotient Rule derivatives and HOW TO TAKE THE DERIVATIVE of a function using the DERIVATIVE RULES (Power Rule, Product Rule, Quotient Rule), jump to: https://youtu.be/QqF3i1pnyzU

The Quotient Rule (calculus) tells you how to find the derivative of rational functions (a fraction, or one function divided by another function). The formal definition (textbook definition) of the Quotient Rule is often unnecessarily complex and intimidating.

There is a memory trick, or mnemonic, for how to remember the Quotient Rule formula. All you need to remember is the song "LO dee-HI minus HI dee-LO, over LO LO," where "dee" means the "derivative of." "HI" means your top function in the numerator, and "LO" means your bottom function in the denominator.

In other words, multiply the bottom function times the derivative of the top function MINUS the top function times the derivative of the bottom function, then DIVIDED by the bottom function times itself. After you differentiate the function with the Quotient Rule, remember to simplify the expression as much as possible using algebra.

This video is a basic intro to the Quotient Rule. For more of my calculus math videos and examples of taking derivatives, differentiation rules like the chain rule, differential calculus, basic calculus, integral calculus, common derivatives, and calculus problems (including Calculus 1, AP Calculus AB, AP Calculus BC, and Calculus 2), as well as precalculus and algebra math help, check out: http://nancypi.com

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• Proud to say first

• actually u got second sorry pal

• @Mark i tried

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• first ish

• hello thanks nancy

• Good video

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• Nice video!

• Love you! I hope you will add some videos about integrates and complex numbers soon👌🏼☺️

• I know how do derive and integrate, and thanks to you Nanci I know what derivatives is, but get i confused when dy/dx is used, when we integrate we write £ f(x) dx, what does dx stand for, what does with respect to time with respect to displacement mean.

I understand maths better than physics, thanks to your precious videos I understood the relation between position, velocity and acceleration.
But I get very confused with Work, energy , & force

But most importantly, i need to know what “with respect to means” or how to get what we want by integration or deriving

I am just frustrated

Had to put down every thing from my shoulder

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• I never remember the quotient rule. I simple use product and chain rule to re-derive it. This is what you must do if you have two functions f,g: R^nto R^m, because “division” no longer makes sense. Instead, you multiply by the inverse matrix. Also, since derivatives are matrices (linear transformations) in higher dimensions, multiplication is not commutative, and the quotient rule will not resemble the one dimensional quotient rule.

• I can 3D print stuff for you but idk what would represent her in the form of merch.

• Hey Nancy! Could you plz do a video on how to find derivatives on a graph from function? Thanks

• easy just find the slope at the point

• Thanks so much!

• fan tastic

• But what if I cant yodle?

• You are amazing

• Hey Nancy, I know you did a video on Inverse function already but I’m taking pre-calc now and I have a inverse function problem to solve which includes Natural Logarithm. If you have time, would you please explain that in a video? Thank you very much 🙂

• You either know math frontwards and backwards, or you are an inspiration to dyslexic people everywhere.

• Nancy hot as always

• M Cai subscribe me

• I like to write the denominator up instead and use a negative exponent, After a while you’ll even forget the quotient rule exists

• You just solve my biggest problem

• Can you do a video on standard deviation? My online professor didn’t go over it enough.

• Thanks Nancy – I DO like math – and I DO like your videos!

• Im so so happy that a classmate told me bout you! Granted it was hearing boy talk and then how you explain things to an understanding level that anyone can understand.
Thank you thank you

• @NancyPi thank u for the awesome vids they helped me with my school work alot. U are alot better than my math teacher 👍thank u and keep up the great work!!!:)

• hey nancy could you do a video on square roots? i have an algebra ii problem that is (y+2)^2=16 and have no idea what to do but my teacher says to square root it

• a square root cancels out the exponent which will just leave you with y+2. but you have to use the square root on the 16 as well because you have to do the same thing to both sides. the square root of 16 is 4. at this point you should have y+2 = 4 and then you can solve for y. the answer is y = 2 and you can verify this by plugging it back into the equation. you probably figured it out by now but I just wanted to help 🙂

• thank youuu!!! :))

• I have a video on this problem. You can check out my playlist

• I don’t understand how people dislike her videos even once, she literally is the reason I passed so all my math courses. Let’s go NancyPi

• Daniel Thompson subscribe me

• They’re proof that there’s pure evil in this world.

• Thank you for these videos! The quotient rhyme is almost the same as my teacher taught us but instead of “Lo * Lo”, he said ” Square the bottom and off we go!” It rhymes well with “High dee low”. Might help somebody else to remember these rules!

• Can you make tutor for s2 hypothesis

• I didn’t even know women like this exsisted… must be very rare.

• can you please make second fundamental theorem of calculus?

• Thanks alot Nancy!!

• Love from India. Mam ur teaching methid is very easy and understandable

• please create an easier version of the product rule :)) this made every problem easier for me!

• Andrew you can use u’v+uv’. u and v are the original functions and then u’ and v’ are their derivatives.

• thanks!

• @NancyPi Can you do a video explaining instances of the Product Rule and Quotient Rule being used in the same problem?

• I learned it almost the same but just a little different ” Lo De Hi – Hi De Lo, Over whats squared below.” It rhymes a little more so it might help you remember it a little more.

• Mine was “Lo De Hi – Hi De Lo, square the bottom and away we go!”

• Professor Leonard uses the same rhyme

• thank you so much 🙏 this helped so much

• I heard of this short but idk I find the normal one easier to remember lol

• Thanks for the calculus video it really really helps especially when your explanations are easy to understand compare to my professors. Thank you for your video and I hope you continue making calculus videos because they really really do help a lot

• Here is your fan from Hong Kong. You help me a lot in calculus.

• Hi Nancy, could you take a video about derivative of inverse function?

• thank you so much you are explain in very easy way i understand the derivative very well ^_^

• im in grade 7 and literally skipped to high school

• +George Washington Dude you’re awesome I think you’d be a good president for that reason

• Nancy you looked different

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• Am I the only one noticing that Nancy can write backwards? Amazing and impressive.

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• Nancy I love you!!!!!!!! Thank you!!!!!!!!! made remembering this so much easier. You’re awesome!!!!!!!

• This video is 3:14 long. But also very helpful. Thank you.

• it’s actually 3:13. but also very helpful. Thank you.

• Orion McGann 3:14 to me

• Well what can you say 😊 it’s NancyPi

• Can you do a video on Infinite Series?

• Thank you Nancy this was very helpful I really appreciate your work

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• Just a 15 year old dude doing those stuff

• absolute legend

• The way I learnt the quotient rule was to do heaps of examples until it became 2nd nature.So it is no big secret ,I found the Khan Academy the best place to practice.

• I mean i guess but if you’re doing maths at this level U should be able to remember such a simple formula

• This is high school maths, dude.

• @timcritt I’m in high school. I always found this pretty easy.

• @HSCMACE That’s my point. It’s easy.

• Hey Nancy Pi I just watch your video’s because your talking has a soothing effect on me. And I learn a thing or three. So thanks, Mitch.

• Mitch Swanson subscribe me

• And if you forget the formula, you can figure it out by writing the quotient as f(x) x 1/g(x) and using the chain rule to differentiate 1/g(x)=(g(x)^-1 and then the product rule. And even the product rule can be derived from the chain rule, … and I think that once you understand the complex exponential function you can get everything from that, so you discover that when you get to complex analysis in arbitrary vector spaces then you don’t need to know any of this complicated stuff, … see

• I’ve never watched your videos but NancyPi and google said 3:14 run time and “Made Easier.” Ok, you deserve the watch!

• Bruuuuuuhhhh!!! This is sooo much better! College professor literally complicate this rule for no reason 🤦‍♂️ Thank You so much 😊

• week 1 of watching NancyPi: Hmmm, a beautiful girl that teaches math
week 2 of watching NancyPi: God, she’s really beautiful but she can solve *insert harder math problem*
week 3: *insert hard math problem* NancyPi

• Thank you soooo much u saved my time!

• thanks

• Holy crap thank you so much I had no idea that “dee” was derivative…. I guess that’s what happens when you don’t pay attention in class

• hehe

• Great teaching as ever. Thanks.

• NancyPi’s videos are proof that sometimes people accidentally click on dislike when they meant like. There can be no other expiation.

• Thank you very much Nancy, I was struggling for 20 minutes, but after watching your video, I understand in 2 minutes, Thank you

• Nice lecture

• thank you so much nancy

• I derived the quotient rule by considering the function “1/LO”, then using the product rule of HI and 1/LO with chain rule.
It might not be quicker, but you won’t make a mistake if you know your products and chains.
P.S. in my region the quotient is taught d[u/v]/dx = (vu’-uv’)/v², and it actually rolls right off the tongue! “vee dee yuu, minus yuu dee vee, all over vee squared.”

• or: vee yuu prime minus yuu vee prime over vee squared

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• thanks

• Hi Nancy,

• The 26 dislikes are from the math teachers who want us to suffer.

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• Beautiful inside and out!

• Down d up minus up d down all over down down

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• This is a great refresher for tutoring. Cheers!

• Her mirrored writing skills are seriously respectable

• Can you please cover Calculus: Higher Order? And with examples using radicals?

• ur the best. thank u

• I remember: “LoDhi, HiDlo, bottom squared good to go”

• love it

• Shes takin over my searches now. Used to be the bald chill teacher guy. Forgot his name.

• You dont post videos anymore ):

• Hi nancy, I’m here because YOU are pretty as fuck

• We learn this in 9th grade calculus class in my high school. When do you guys first learn quotient rule?

• Thank you

• As a math major I really don’t believe in the Hi Lo J-lo rhyme. It making matters worse. It’s just more formula to remember. You should just remember the quotient rule which isn’t that difficult and it should become natural to you.

• Excellent Series Nancy – You are the best maths teacher in YouTube.
Will you please do a series of lectures in
1) Permutations and Combinations
2) Statistics basics and Probability
Thanks

• i know all the calculus lesson and while seeing this video i get confused that much bad is this video

• This method is really catchy but I was able to use it and come up with my own method