Derivatives... How? (NancyPi)

MIT grad shows how to find derivatives using the rules (Power Rule, Product Rule, Quotient Rule, etc.). To skip ahead: 1) For how and when to use the POWER RULE, constant multiple rule, constant rule, and sum and difference rule, skip to time 0:22. 2) For the PRODUCT RULE, skip to 7:36. 3) For the QUOTIENT RULE, skip to 10:53. For my video on the CHAIN RULE for finding derivatives: • The Chain Rule... How?... For my video on the DEFINITION of the derivative: • Derivatives... What? (... Nancy formerly of MathBFF explains the steps.
For more of the QUOTIENT RULE and a shortcut to remember the formula, jump to my video at: • Quotient Rule Made Eas...
For
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What is the derivative? It's a function that gives you the instantaneous rate of change at each point of another function. You can calculate the derivative with the definition of the derivative (using the limit), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule:
1) POWER RULE: If the given equation is a polynomial, or just a power of x, then you can use the Power Rule. For a term that's just a power of x, such as x^4, you can get the derivative by bringing down the power to the front of the term as a coefficient and decreasing the x power by 1. For example, for x^4, the derivative is 4x^3. If you have many terms added or subtracted together, and if they are powers of x, you can use the Power Rule on each term (by the Sum and Difference Rules). NOTE: The derivative of a constant, just a number, is always 0 (that is the Constant Rule). Also, if you have a term that is a constant multiplied in the front of the term, like 2x^3, you can keep the constant and differentiate the rest of the term. In this example, you keep the 2 and take the derivative of x^3, which is 3x^2, so the derivative of the term 2x^3 is 2*3x^2, or 6x^2. ANOTHER NOTE:You can use the same power rule method for fractional or negative powers, but be careful... for negative powers, it works as long as x is not 0, and for fractional/rational powers, if the power is less than 1, your derivative won't be defined at x = 0.
2) PRODUCT RULE: If your equation is not a polynomial but instead has the overall form of one expression multiplied by another expression, then you can use the Product Rule. The Product Rule says that the derivative of two functions multiplied together is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
3) QUOTIENT RULE: If your equation has the overall form of one expression divided by another expression, then you can use the Quotient Rule. The Quotient Rule says that the derivative of one function divided by another (a quotient) is equal to the bottom function times the derivative of the top bottom minus the top function times the derivative of the bottom function, all divided by the bottom function squared. This is true as long as the bottom function is not equal to 0.
For more of my math videos, check out: nancypi.com

[@arianahouman7914]

Why go to college and get confused for hours when there's a free 15 minutes video that explains everything? We need more teachers like you!

[@shedimale1967]

hahahahahahahahahahahahahaha...that's right!

[@dariansoobramoney8926]

Exactly, she's amazing

[@hughpearson3191]

I agree and disagree.. 3blue1brown video's are much easier to understand and when they show a derivative, they also break it down to real world numbers and come up with.. an ANSWER :) They use sophisticated animated graphs and the presenter has a very very friendly voice.

[@Dan-tv1sm]

@@hughpearson3191 But the tutor isn't so pretty and captivating. She really keeps my attention focused.

[@hughpearson3191]

@@Dan-tv1sm haha.... I get it, but being captivated by looks does not improve our understanding :) Nancy does have a very warm personality.

[@erichomsy]

i figured it out. when she's filming she writes the equation out so its legible to her and then mirrors the video in post. genius

[@ValeriaMedina001]

HAHAHAHAH I was wondering too thanks

[@ismaelsaintfleur1778]

Lmfao im glad im not the only one that was curious about that

[@corey1064]

duh?

[@teaman7v]

Bless you

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Not at all she’s literally behind a pane of glass

[@mcorona0710]

I took calculus last semester and had to drop it, too complicated. Gave it another go and stumbled across Ms NancyPi and I'm killing it with a straight A. She helped me understand in less than 20 minutes what I couldn't over an entire semester. Just simply awesome

[@mevadavraj4178]

I think this video is very basic for you as you are university student, if I am wrong don't take me seriously

[@ticskitmusic656]

@@mevadavraj4178 it is, I'm in engineering school but once you've understood these you're kinda good to go, it's somewhat similar to understanding the language of a text book.. So you would learn the basics and then the entire text book is in the language which now, you know. As long as you don't rely completely on this because there are Ln and log rules as well as an entire hell of trigonometry, you're good. All you have to do is look them up and practice

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Im taking Calculus in college right now and after class I basically re-teach myself using your videos thank you so much!

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same

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Her and organic chemistry tutor

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Like honestly, WHY aren't experienced college professors as incredible as teaching as this young student!?

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Because (at least at universities) they are hired for their research skills and not for their educational skills. Contrary to popular belief these are not the same thing. Knowing a lot doesn't automatically mean you can teach it.

[@shedimale1967]

Yeah

[@ronclass1782]

Because it is one of the most stable careers so they don't care

[@hughpearson3191]

haha... maybe because they cannot SPEED write like Nancy when she speeds up the video sometimes ;) Its like she has superpowers eh!

[@juicynugget]

Because they give you the general idea of how to do it and don't elaborate much

[@yourverdict5405]

Thank you so much for posting again you literally got me through highschool math....im in foster care and ended up going to 6 high schools in4 years....literally you are the only reason I passed math

[@snakebitTim]

Keep it up! Nobody can buy knowledge.

[@hughpearson3191]

I still recommend 3BLUE1BROWN as an other helpful site. Nancy is good.. really good..but she tends to rely a bit on knowing rules rather than deeply understanding the issue. That's probably a confession about my cognitive abilities though hey :)

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You should attend a church... Not all are the same, some actually help people like the one I go to 🙏

[@harryalvarado9041]

@@hughpearson3191 Yup

[@2xXaylaXx2]

@@hughpearson3191 I think both complement each other. These conceptual videos like on the channel you suggest give a deeper understanding of what's actually going on and then NancyPi helps with the application of their rules so to say :)

[@aleynan2153]

I seriously didn't think I'd ever understand this based on the way my professor taught it but the way you explained it is so simple. Thank you!!!

[@Wormy0172]

Nancy, your videos make learnbing math so easy. thank you for your hard work and attention to detail! it does not go unnoticed. I'm so excited to keep learning from this channel :)

[@juang.138]

my professor uses your videos to make sure we understand the lecture he just gave. Thanks for helping with my H/W.

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😆

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Plot Twist: Your professor is Nancy *then you wake up and realize its a dream*

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Thats a sign of bad teaching whcih would give a reason for a clever student to change uni

[@user-qv3bu8ud9o]

professor is simp 😆

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I found myself drowning in a machine learning course and would have been dead in the water without your videos. Thank you so much for literally the best explanations and demonstrations I have ever seen. I can't wait to watch the rest of your videos to get caught up with math again! Thank you!! :)

[@sophiedallimore8938]

You're one of the first people to make calculus make sense to me, thank-you so much!

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OK! to be completely honest, this is absolutely amazing. I have been looking for a teacher like you and I'm so glad I've you. I never thought I'd ever understand calculus but you've helped me a lot. Thank you so much 🙏👏 Please keep up the good work.

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You're a walking angel. Thank you so much for your videos. I love how you are able to dummy it down. I've literally gotten thru calculus off of just your videos.

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You're an amazing teacher! I have a calculus test today and your videos have saved me. You've earned yourself a new subscriber! Kudos!

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Started studying mathematics after 15 years for my PhD economics courses, and your videos are truly the saviors for me. You explained in a brilliant way, thumbs up.

[@BearShaman1]

Fantastic content. Very concise and fast-forwarding through the writing is wonderful since that's honestly what kills me about other math videos.

[@stangabay1707]

Ok, I'll say it because we're all thinking it. Smart and beautiful! Thank you for taking the time to show us how to do derivates in a very simple and understanding way! No math-ese. You speak our language! Thanks, again!! :)

[@caseses]

When I graduate from my MSc, I legit am going to acknowledge your contribution. Thank you for saving so many tests

[@TheSarenarass]

also msc gang watching this video

[@donaldbarker6380]

What an amazing young lady. Half-way through my Applied Calculus course and I understand FINALLY, why I subtract F(x) and why Quotient rule works. Well done!!!

[@wellnesshearddifferently5920]

Love how you edited & explained the concepts so well. Calculus is definitely our favourite with you;)

[@tolineee]

Literally wish you uploaded these before I failed my class two year ago, you are so composed and make it really easy! I took the class again this year and did really well on my last exam. Thank you never stop with these.

[@usamarafieck1715]

I would never known this 2 years ago.

[@zacharyschoen1877]

Solid video. Haven’t revisited math in years and you simplified it and described it bare bones 🦴 just the facts🤙 thx

[@cabreracelina]

You have no idea how grateful I am for your videos!! Thanks NancyPi!

[@MaThalent]

Im very happy that ive found your channel. I need this to refresh my math. Thank you for your very simplified lessons.

[@DonDOSS_]

who can explain in so much simpler terms . you are amazing in teaching and beautiful as well .lot of bonuses in one shot . thank you .

[@XXAbbott]

I just graduated college and my math class was the hardest class I took in college (I'm not good at math) but derivatives are really cool, i find myself doing them for fun because the numbers you come up with are really cool and its kinda a mystery how this was created. Great video, wish i would have found this a few months ago when i was struggling with them lol.

[@DN-ps4bn]

I appreciate your effort ! It’s makes studying much easier ! I don’t have time to go to class most days and you’re better than textbooks !

[@fionamariepapna4109]

Thank you so much Nancy! You are such a great help for every student who wants to learn in the middle of a pandemic.

[@stephanieirissapno9746]

Omg i was like absent minded when my teacher was discussing this and it was so boring, his voice was like a lullaby. Thankyou so much for this i completely understand it now

[@usamarafieck1715]

Reading the textbooks is more harder than listening to this.

[@robynm15]

Actually going through cal 1 right now so much appreciated.

[@matthewblonder8512]

Robyn Martinez ab or bc?

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I got bc, because I need to train for business.

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Matthew Blonder calc 1 is just the general college calculus class however in high school calc 1 is basically ap calc ab

[@user-yr3uj6go8i]

Same. I have my test on derivatives tomorrow in college...

[@CIDteenie]

OMIGOD THANK YOU!!! ❤️❤️❤️ I'm so grateful for the clarity of your videos. This was something I was positive I'd never understand and now I get it!!!

[@mylittlebouquet3994]

OMG THANK YOU SO MUCH, I had this math assignment due tomorrow and I didn’t learn anything about derivative in class, looked for the answers to my questions from Khan Academy but after watching almost half of the video classes I still didn’t understand anything but this, THIS HAS HELPED ME! DERIVATIVE IS EASY AF THANK YOUUUUU

[@1zDiegoz1]

You’re helping me out so much. Thank you for people like you🙏🏽

[@tootoophoto]

Nancy, you are amazing! thank you so so very much for making this so simple!

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watch my maths tricks.

[@ramontogonon1119]

I already know derivative but you're worth watching. Wonderful teacher by the way you deliver the lesson always facing the audience. God bless!

[@aicexy2974]

Thank you for being straight forward to the topic and so clear to explain it. You help me a LOT. Thank you 💯❤

[@koxukoshu]

"you probably should do that... because reasons" truly

[@franklaurn9068]

Smart, beautiful, and a great teacher! So glad you are posting again Nancy. You are the best!

[@JD-ye2pw]

I'm really enjoying this. Thanks a million Please don't stop making these vids

[@Bee-vq6pl]

You are the most helpful human being when it comes to math. Thank you!

[@ImKurono]

I missed her :D Can’t wait for more videos. I got to go through calc 2 during a summer semester. Refreshing on calc 1 and self teaching calc 2 until I take it will help retain information.

[@samuelrosenberg5088]

This helped me a lot. My professor has a really traditional way of teaching, and it is extremely hard to follow sometimes. This video cleared up a lot of stuff for me, thanks!

[@unleashedgamingmaster]

Thank you Nancy for uploading the video. That was very helpful, now i can easily remember the quotient and product rule. Thank you so much 💕🙌

[@Slimboyfat1979]

You are changing lives. You are an amazing teacher. Thank you.

[@ericacuevas2301]

Damnit Nancy I've been so confused and this just makes sense! Thank you.

[@Noosic]

I tried to teach first semester calculus when I was a second year medical student for my community medicine rotation and I must not be a good teacher. I was frustrated the first week after only two classes. To be a teacher of any subject is truly an art and a skill. Time to give teachers their due.

[@neiltoersbijns2921]

Nancy these videos are awesome we all really appreciate them.

[@camerondavis8182]

Thank you I have an exam next week and derivatives made zero sense to me I thought it was a function on the calculator but this cleared everything up. God bless you!!!

[@dominiquetricault3406]

hello i'm french and i like your video ,this allows my son to learn maths and english at the same time

[@albertbatfinder5240]

Dominique Tricault You make a good point that English speakers might not notice. NancyPi is a talented educator not just because of her maths knowledge, but also because of her clear use of language.

[@resikin]

“Ah romance, I am French,”

[@jayfizzle5721]

Love that your back on KZbin 😍

[@wasifarshad5095]

Thanks Nancy. Quiet simple way to remember the differentiation once again.

[@dinu7355]

Really Great Tutor on KZbin, wow this type of tutor is amazing for all the students... I have learned a lot from this video thank you so much for your support

[@abrielhijara9859]

Hi! Nancy. :) thanks for this video. I learned a lot from you. You're even better than my previous teachers. Yeah, not to mention those people.

[@jentoons7565]

WTF This explained so much more clearly in 15 minutes than my hour and 20 calc class

[@AntificationAdam]

Thanks for taking the time to explain things slowly! everyone else seems to rush through the workings and I just lose track of where everything is at.

[@seaknightvirchow8131]

I am retired. i took calculus 45 years ago and I have forgotten most of it. I have decided to relearn my basic math beginning with algebra and trig. These videos, even calculus, are bringing back so much of what I had forgotten. You are a very good teacher. Somehow these concepts are now easier to understand than when I first encountered them and though part of it is dusting off the once learned material, I think it is also due to how you explain things so clearly.

[@thecosmiccube8178]

If you have the will to learn, then I think you are ought to learn about history, art, psychology, economy, religion, politics and near these topics. I suggest you read books about them. It's better to teach and share knowledge with younger generations so they may improve their life more and take guidance from you. It is easier and more beneficial than math.

[@seaknightvirchow8131]

@@thecosmiccube8178 I

[@seaknightvirchow8131]

I have a library of 3000 books read over a lifetime and it includes all those topics you mention. I encourage my sons and grandchildren to read and I give them books. Besides history, art, philosophy, theology, I love science which is why I am relearning my math. I am comfortable with molecular biology but less so with physics. I can also help my grandchildren with algebra and trig. I think your advice is sound overall, except the math part. 😉

[@thecosmiccube8178]

@@seaknightvirchow8131 Nice, how rare is to find someone alike you!

[@thecosmiccube8178]

@@seaknightvirchow8131 From my point of view, I think physics for practical life, is more useful and helpful than molecular biology. It makes you realize the concrete world around you and how you can interact with it effectively, but mostly from its concepts and terms, not mathematical equation.

[@samanthat.4281]

Yay, thanks for posting! ^w^ I’m in college now, but I remember your math videos helping me so much in high school calculus! :) This video helped me brush up on my math-thanks a lot!

[@aceplusplusplus7652]

Thank you so much! I found that really helpful and to understand the product rule (without any sort of confusion!) in such short amount of time!

[@jacobp2751]

You are amazing!! Best video I've found explaining how to use derivatives!

[@marcusknight3862]

Her voice is so gotdamn soothing lol. More importantly, she explains these concepts in a no-nonsense fashion. Very helpful.

[@johnpro2847]

sure is ..i fell asleep

[@Klimawandel20]

wow, she is so laid back. never seen so much calmity.

[@CorpusLael]

Nancy is saving my life in Calculus 1. Thanks a lot!

[@julesl6910]

I keep coming and coming back to this channel, I can't stop coming

[@RaffaelloLorenzusSayde]

Thanks so much for helping me ❤ I was totally lost in this part of calculus. Especially the new notation used confused me.. our teacher didn't explain what those notations meant lol 😅

[@liamhopkins29]

"You should probably do that because... reasons" - Nancy Pi 2018, AND My Calculus Prof 2019

[@DrSamsHealth]

An absolutely divine explanation!

[@dominicheywood1883]

Hi Nancy I love watching your videos especially on how you explained the derivative I never learnt the true meaning until you pressed the truth about how the formula came out .

[@daliamae3430]

Dang Nancy. You're just pushing out videos. You go girl

[@ankhbolddugersuren4330]

Having a beautiful teacher is so nice xD .. Thank you so much

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This is amazing great content I like the way you explain your steps easy to understand and grasp the concepts.

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Thanks. Good luck ❤❤❤ We need need teachers like you!!! Keep going...👌👌👌👌

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I LOVE THIS WOMAN YOU HAVE NO IDEA HOW MANY TIGHT SPOTS IN COLLEGE SHE HAS BAILED ME OUT FROM!!!!

[@Kqrl69]

how are you writing backwards

[@tommyvercetti1210]

She isn't

[@redsusoverparadise2700]

Yes she does, but computer stuff is possible

[@bozzigmupp510]

bruh she is just flipping the video

[@Toxicblackmambahs]

in her Q&A she said she knows magic and can't tell us her secret

[@SDJ99200]

She writes on glass and then just flips the video, wow magic

[@user-li4zh9mf4t]

Every time i watch gives me a big confidence. Thanks for this video showing.

[@barungijoyhanah7423]

I know this is an old video but five years later it feels so new.... Thanks NancyPI❤❤

[@xlovelyvintagex]

Nancy... you’re saving me lady 😩... wish you could replace my calc teacher 🙄

[@usamarafieck1715]

I needed this.

[@Noneblue39]

i remember back in the day where i had to do them by limits ... also is there a video on partial derivatives?

[@imperialrecker7111]

i am still using it 😀.

[@humanfrommars5832]

Watch professor Leonard

[@pandaonsteroids5154]

I like your videos. You talk like you're feeling the pain with us. Plus they're painfully simple. I really like it.

[@blitzblutz]

You make it so easy Nancy!

[@aneesurrehman9832]

Nancy thanks for being such a perfect teacher,t love from pakistan.

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I didn't understood at all, but enjoyed every second of it 😁😜

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Amazing. Thank you for the great job. Best math channel ever

[@jacobchanda4405]

Thankyou so much Nancy 💚💕💖 Your Tutorial videos are the best!!!!

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"You don't have to like math but you can like my video so if you did, please click like and subscribe" that transition was so smooth. just as linus' transitions to his sponsor, private internet access

[@jayraskin]

Nice. I'm studying calculus on my own, just for the fun of it. This made things very clear for me.

[@Elliephh]

hey! me too!

[@justanotherguy469]

I love calculus and I love your videos. Thank you for taking the time.

[@deck2296]

Thank you so much for this video! This helps so much

[@alicelevert2325]

@NancyPi can you explain when you work out a problem. can you go through the steps?

[@donttakemeserious3467]

Calculus has suddenly become more interesting😍

[@naderhumood1199]

You outdid yourself today. Million thanks.

[@sinitey_natey2]

loved how you make it look simple!.

[@theheadshot45]

Please please please make an Eigenvalues and Eigenvectors video.

[@mokgadisekhaulelo3420]

can we swap brains for my upcoming calculus test ,i promise i"ll bring it back

[@Mr.Weeast]

This seriously helped so much. Thank you.

[@Vikermajit]

Finally beginning to understand calculus. God bless you, Nancy.

[@shafe9866]

“...it will come back to haunt you” haunts me every time

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its her apparent catch phrase if you've watched more than one of her videos lol

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can you please do a skincare video though

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Her skin is glowing.

[@diyahashem9447]

Thats what make her special As a beautiful girl she is still not making her self as the other beautiful girls Only a model for experimenting beauty cosmetic products Finally there is a girl who wants to save the world from math

[@schanemassey3861]

its called washing your face You moron!!! Its not that hard...lol sheesh you must walk around with musty pits, stank butt and horrid breath?!

[@FranciscoGarcia-fn1vs]

Yet again, an amazing explanation!

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I have a calc exam tomorrow and you just made this SOOO much easier to understand !!!TYY

[@dv5217]

"You probably should do that, because... reasons." My list of reasons: My professor's reasoning: "You're totally right! You don't **have** to do it. But if you **don't**..." _cue decapitation, disembowelment, and confused screaming_