Quotient Rule Made Easier (NancyPi)

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

Follow Nancy on Instagram: https://instagram.com/nancypi
Twitter: https://twitter.com/nancypi

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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  • Ꜳ I 4 years ago

    Proud to say first

    • Mark 4 years ago

      actually u got second sorry pal

    • Ꜳ I 4 years ago

      @Mark i tried

  • Abel Lopez 4 years ago


  • Mark 4 years ago

    first ish

  • Mark 4 years ago

    hello thanks nancy

  • Joseph Joy 4 years ago

    Good video

  • Mr Ch33seHed 4 years ago

    Idk HOW i missed this video before but thanks for this! 🤗💕

  • Amit Majoka 4 years ago

    I love you Nancy

  • Leonardo Camargo 4 years ago

    Nice video!

  • Maggie Stankiewicz 4 years ago

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

  • Joseph Joy 4 years ago

    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

    • Mark 4 years ago

      its nancypi

    • Joseph Joy 4 years ago

      Am sorry 👍

    • Mark 4 years ago

      I was joking your good

  • Mark 4 years ago

    yo can we get nancypi merch pls nancypi pls give us merch

    • Caleb Nastasi 4 years ago

      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.

    • John Carl 3 years ago

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

  • fearLESS 4 years ago

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

    • Mark 4 years ago

      easy just find the slope at the point

  • Kayla Wagner 4 years ago

    Thanks so much!

  • OrphanPaper 4 years ago

    fan tastic

  • Monti 4 years ago

    But what if I cant yodle?

  • Surajuddin Mondal 4 years ago

    You are amazing

  • James Corden 4 years ago

    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 🙂

  • Jerry Gundecker 4 years ago

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

  • Dududu C 4 years ago

    Nancy hot as always

    • SL maths.lk 3 years ago

      M Cai subscribe me

  • Juan Villota 4 years ago

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

  • Ahmed Mzhr 4 years ago

    You just solve my biggest problem

  • Lonewolf 4 years ago

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

  • Graham Phillips 4 years ago

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

  • DaG1nG3rN1nJA 4 years ago

    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

  • Anthony Tang 4 years ago

    @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!!!:)

  • strawberry bob 4 years ago

    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

    • Aniya M 4 years ago

      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 🙂

    • strawberry bob 4 years ago

      thank youuu!!! :))

    • Greesha 4 years ago

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

  • Daniel Thompson 4 years ago

    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

    • SL maths.lk 3 years ago

      Daniel Thompson subscribe me

    • The Black Lodger 3 years ago

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

  • Christian And Kaya 4 years ago

    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!

  • Sohail Fatadin 4 years ago

    Can you make tutor for s2 hypothesis

  • Cody Brown 4 years ago

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

  • Minju Lee 4 years ago

    can you please make second fundamental theorem of calculus?

  • Kamran Ahmed 4 years ago

    Thanks alot Nancy!!

  • Sachin Ugale 4 years ago

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

  • Andrew 4 years ago

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

    • That Random Kenyan 4 years ago

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

    • Andrew 4 years ago


  • iCeD 4 years ago

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

  • KIX IX 4 years ago

    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.

    • DjSpunz 4 years ago

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

    • Gerardo Leon 4 years ago

      Professor Leonard uses the same rhyme

  • d c 4 years ago

    thank you so much 🙏 this helped so much

  • Jorge Guizar 4 years ago

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

  • Alfonso Dominguez 4 years ago

    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

  • ben jjm 4 years ago

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

  • Celine Lo 4 years ago

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

  • Gin Mo 4 years ago

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

  • George Washington 4 years ago

    im in grade 7 and literally skipped to high school

    • Kevin vs. Gamingz 3 years ago

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

  • norbe norbs 4 years ago

    Nancy you looked different

  • Chelsea Mohammed 4 years ago

    bless her soul

  • pamodha wickramarathna 4 years ago

    of my god your lessons are really helpful.

  • Jason Grischkat 4 years ago

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

  • ben-hallel chidanhika 4 years ago


  • RahulTheTechGuy 4 years ago


  • Jae Bro 4 years ago

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

  • Gravey 4 years ago

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

    • Orion McGann 3 years ago

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

    • Totoro 420 3 years ago

      Orion McGann 3:14 to me

    • Kevin vs. Gamingz 3 years ago

      Well what can you say 😊 it’s NancyPi

  • Alexander Quilty 4 years ago

    Can you do a video on Infinite Series?

  • CK Mwiinga 4 years ago

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

  • joe duru 4 years ago

    she’s hot

  • Jennifer Lee 4 years ago

    Thanks for all your help in math you r a genius😊 please comment back! You will make my day lol

  • Terrence Lau 4 years ago

    Just a 15 year old dude doing those stuff

  • Chemical Confusion 4 years ago

    absolute legend

  • syd barnes 4 years ago

    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.

  • HSCMACE 4 years ago

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

    • timcritt 3 years ago

      This is high school maths, dude.

    • HSCMACE 3 years ago

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

    • timcritt 3 years ago

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

  • Mitch Swanson 3 years ago

    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.

    • SL maths.lk 3 years ago

      Mitch Swanson subscribe me

  • Ian Grant 3 years ago

    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

  • Chris R-M 3 years ago

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

  • Abdul-Latief Omar 3 years ago

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

  • Skrmng Hrd 3 years ago

    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

  • Somaya Alhadi 3 years ago

    Thank you soooo much u saved my time!

  • Jhay Dela Torre 3 years ago


  • Ben Eastman 3 years ago

    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

  • Sara Martin 3 years ago


  • Christina Jacobe 3 years ago

    Thank you so much! I missed my lecture about this and was super confused about the “lowdeehigh” thing people were talking about

  • Peter Hunt 3 years ago

    Great teaching as ever. Thanks.

  • Albert Batfinder 3 years ago

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

  • Vishu Bhatnagar 3 years ago

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

  • Kaihii Aleshiikho 3 years ago

    Madam I like your beauty

  • Engineer suleman 3 years ago

    Nice lecture

  • tugsu tugsu 3 years ago

    thank you so much nancy

  • MountainC 3 years ago

    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.”

    • MountainC 3 years ago

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

  • atlas mubeen 3 years ago

    bohat accha samjaya hai

  • atlas mubeen 3 years ago


  • Shahid Khokhar 3 years ago

    Hi Nancy,
    Can you please make tutorial videos about differential equations also?

  • Aseya El-M 3 years ago

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

  • Shivank Pratap Singhal 3 years ago

    Beauty with mind!👌😁

  • Mike Jouhari 3 years ago

    Beautiful inside and out!

  • Shoe Chew 3 years ago

    Down d up minus up d down all over down down

  • nothereforlong 3 years ago


  • seanparsa4 3 years ago


  • Aaron Stewart 3 years ago

    This is a great refresher for tutoring. Cheers!

  • Shengjie Xu 3 years ago

    Her mirrored writing skills are seriously respectable

  • Jess Morales 3 years ago

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

  • Ali Aboushaaban 3 years ago

    ur the best. thank u

  • Odiggidydog 3 years ago

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

  • Akshaymech Ahlawat 3 years ago

    love it

  • John Carl 3 years ago

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

  • TinaKelly 3 years ago

    You dont post videos anymore ):

  • Papi Salas 3 years ago

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

  • Andrew M. Gonzalez 3 years ago

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

  • Tony Burnett 3 years ago

    Thank you

  • espn168 3 years ago

    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.

  • Bharani J 3 years ago

    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

  • sivakumar korimilli 3 years ago

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

  • Gabriel Agbemey 3 years ago

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

Comments are closed.