MIT grad shows how to find the tangent line equation using a derivative (Calculus). To skip ahead: 1) For a BASIC example, skip to time 0:44. 2) For an example that uses the QUOTIENT RULE, skip to time 5:58. 3) For an example that uses TRIG FUNCTIONS and the CHAIN RULE for finding the equation of a tangent line, skip to time 11:35. Nancy formerly of MathBFF explains the steps.

For HOW TO FIND DERIVATIVES, jump to: https://youtu.be/QqF3i1pnyzU

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What is a tangent line? It is a line that is tangent to a curve at one point. You can use calculus for finding the tangent line equation, by taking the derivative of the given function.

Finding the EQUATION OF A TANGENT LINE using a DERIVATIVE:

There are four main steps to find the equation of a tangent line with derivatives:

1) TAKE DERIVATIVE: The first step is to take the derivative of the given equation, with respect to x. For instance, to find the equation of the line tangent to f(x) = x^2 + 3 at x = 4, first take the derivative of f(x), which is 2x, by the power rule.

2) PLUG IN X-VALUE INTO DERIVATIVE TO GET SLOPE: The second step is to plug the given x-value into the derivative of f(x). The value you get is the slope of the tangent line, m.

3) FIND Y-VALUE OF POINT WITH ORIGINAL EQUATION: The third step is to find the y-value of the point. You get this by plugging the given x-value into the original equation to find the corresponding y-value. Since you want the tangent line at x = 4, plug x = 4 into the original f(x), and you get a y-value of 7. Now that you have both the x and y coordinates, this means that the full point is (4,7).

4) PLUG THE SLOPE AND X,Y POINT VALUES INTO POINT-SLOPE EQUATION: The last step is to put the x and y point values, as well as the slope, m, into the point slope equation of a line. The point slope form is x - x1 = m (y - y1). Plug the x and y point values into this equation for x1 and y1. Plug the slope you found in for m. This is the equation of the tangent line. The equation will still have x and y variables in it.

You can also rearrange the equation you get so that it is in "y equals" or slope intercept form, if you want.

You may need to find the derivative with other derivative rules, such as the quotient rule or chain rule. Even if you need to use other rules when taking derivatives, or even if you need to differentiate something like a trigonometry function (ex. secant) or a fraction form with a numerator and denominator (rational function), the four main steps to find the equation of the tangent line will be the same.

For more math help, check out: http://nancypi.com

Welcome back!

Love you! Keep up the good work! 🙂

1

hey nancy, can you make a video on solving optimization problems using calculus?

Yes, videos on complicated and harder calculus problems?

Yes! optimization or related rates..

whew, I still remember calculus

For me it is simpler to consider that there are an infinite number of lines with a given slope (say, 5). That is, lines that satisfy:

y = 5x + b

But only one contains a given point [say (1,3)]:

3 = 5*1 + b

Solving for b give -2, so we know the equation of the tangent line is

y = 5x – 2

I think this method gets students ready for initial value problems and avoids the symbol overload of the 5 variables in the point-slope equation.

you’re a god

Could u do one with horizontal line

how did you get cos(pi/3) is equals to 1/2 and tan(pi/3) is equals to square root of 3?

Thanks, very helpful video

helpful as fuck

2:47 i can’t understand why the slope m is a result from the x-coordinate only?

I am the 101 like 😉 appreciable. very nice explanation

Nice

2:52 “The third step is…oh never mind. Fuck you guys.”

thank u so much madam…

hey Nancy thanks a lot now I can easily solve tangent

how do you write on that i’m perplexed

@YoIts LemonBoy! Therefore, she is not left handed so she may have a wedding ring on. Bummers.

@Hugo Anzola why are people like you so creepy. dude go outside and meet someone or soemthing. stop tryna marry a tutor online.

Hugo Anzola I’m pretty sure she’s left handed

@Hugo Anzola Creep.

@Diego Villarroel she’s right handed.

Or she’s left handed and has mastered writing backwards.

What is most likely?

Bear in mind about 90% of people are right handed also

Do you know any Physics teacher as good as you? 😊

michel van biezen

hey Nancy hope u doing well, actually I jst wanna knw why u love pi so much

Great teacher: very consequencial,slowly speaking and clear. Thank you!

…and pretty, to keep eyes focused on the front of the class…

Completely different from mine

How would you find x^3+3x-2? You did not cover what to do if there was a constant in it?

when using the power rule, you do power times the number and -1 from the power. The constant -2 just turns to 0.

Nancy, your videos are so helpful! They have really helped me through Calc1. But there’s something I must know…

How do you write backwards? It blows my mind every time

She flips the video lol

OMG Thank you so freakin much!!! This rely helped me.

youre honestly the best. thank you so much

I don’t know what you’re talking about but I could watch for hours. My math capability is: Duhhh!!!

Thank u, I love u

Thank you so much for this, it helped me a lot with my homework and hopefully, you have more videos as I get more into calculus.

I just wanted to say thank you Nancy. I am not sure why my professor made this so unnecessarily hard. You are the Math Goddess.

Thank you so much! It’s amazing how simple it all is but I was dying over here trying to figure this out

Thank you very much !!!! Ma’am

Forever I wish you were my calculus teacher!

Can you please do a video of finding the slope of a curve without using derivatives. Using limits plz ;-;

use either the alternate form or the definition of a derivative to find the derivative and go from there. The one with h in it

are you really writing backwards

lol the video is just flipped ..

A tangent to straight line is the same straight line !

please be my calc tutor your a beauty

so hot

On the third example f(x)=(secx)^2 , shouldn’t f'(x)=2(secx)(secxtanx)^2 ??

Can you do some linear algebra videos too? Please Mrs.Teacher 🙂

Her name is Nancy

Or you could write x/(x-1) as x.(x-1)^-1, if you forget the division formula a lot like me 🙂 Then use product and chain rule in order to solve. It is a different function but it works.

Am I completely stupid or just exhausted from a very long day but…how the hell is she not writing backwards on the board?

You are really beautiful and video is very helpful though.. thanks

hey this was so useful!!! Can you do one with tangent lines in regards to implicit differentiation?

Thanks for the effort saved my life!!!

myyy good i loove you sooo muchhhhh

Thank you so much for this information

most beautiful math teacher in my life.

Thank you! This really helped with my hw!

Thank you very much for the concept. The video was in detail and easy to understand.

i got lost at the second question

watch a vid on quotient rule

is this the same as the equation of a tangent?

I think u could be a little more active n interactive… But ur gr8..

Soooo pretty 😍 thanks for the vid !

Thank you!!!!

we have a singer who called nancy she has a nice voice shes pretty good singer

We learned how to do this before knowing what derivatives are, and holy shit it would take like 5-10 mins. This method takes like 1 min thank u so much

Hold on I have a question. Was I supposed to look at the equations ? If yes, then I’m glad I didn’t waste 19 minutes by ignoring the equations and focusing somewhere else throughout the video. If u know what I mean.

hb hb I meant her face, who’s disrespectful now ?

You are a concise, effective and clear communicator. Thank you!

I wish I was being taught by a tutor like you for basic class unto…

If you agreed click like

I swear…if Nancy went out with the youtuber Professor Leonard, (look him up he’s equally awesome) they would have the sexiest babies on the planet…seriously…

And smartest

Thank you sooooo much you are 1000 times better than my teacher

thnks teacher

Madam you are great explain everyone step easily

Beautiful explaination

By constructing a tangent line, we can calculate the slope of a curved line at a given point ? Explain this to me please? Oh and you can have all my pasta. You have an amazing sense of humor in the Q & A.

Score! @NancyPi you make this super easy to understand. Much obliged.

School seems pretty useless when videos such as this one explain it so much better.

I love you so much

Nothing sexier to me than a woman who knows math! Watching you has renewed my love of math. Thanks for the videos!

Imagine a world where all advanced math teachers are hot

Playing the video in 2x speed, still kinda slow

Excellent! Excellent! Just purely excellent!👍😊😃😃🙏🙏🙏🙏🙏🙏🙏👏👏👏 may JESUS continue to bless you with the gift of explanation

Thank you so much🙏🏻 I was so confused

channel is very helpful! thanks a lot!

Thanks a lot

very helpful but for some reason I found it hard to concentrate

can you do a video on logarithmic differentiation? BTW YOU’RE AMAZING! I was so confused until your videos and now it’s simple and makes complete sense.

thanks a lot

Mam…!

why am i watching this video? i dropped out.

If you are being held hostage, blink twice

Oh common she is obviously under hostage situation. But I never seen such a cyber crime where the user is forced to run a channel in order to send secret codes or maybe something for more vivid reason.

@Mohammed Wasey Siddiqui *MARINA JOYCE*

Would you go on TV and say Hello I am Nancy Pi?

Mohammed Wasey Siddiqui Just think of all that YouTube revenue…

Nice one Ma’am 👌👌👌

Thank you! I was super frustrated and couldn’t figure out my homework.

Your student is lucky . Great teacher 👍

Great teacher , beautiful teacher thumbs 👍👍👍👍

Anybody else have a calc test tomorrow? Like if so

@Egg Fair enough, I respect that

It’s 12:47 test is 1 wish me luck fellas

Zeyad Mo7ammed how’d it go man

@Egg /r/iamverysmart

@TMTM *r/ihavereddit*

so this is what you should do when you’re asked for the slopes of the devil’s curve right???

Wait a minute! Are you writing backwards? That’s awesome!! How can you do that??

Franco Ortiz reverse the video u dumbass

She is a queen, ruler of thots, and saviour of those in the war with calculus.

ah i see a man of culture

has she trained herself to write backwards, cause omg thats talented

I feel like the screen is mirrored in editing

they just flip the video in editing dumbass

Absolutely amazing video. Thanks, it was very helpful!

what would you do if you dont have the y value given though?

Solve for it

I have to watch this at 1.5x

Thank you!

Many many thanks mam.

You save my life 💚 ty 😊

I love you

HI Nancy! so what would it be in this case.. Your answer would be greatly appreciated

x ̈ + x + αx3 = 0

α = 0, 2, −2

Regards

i think i’m in love with math xD

I always found point slope formula unnecessarily complicated. I find it much easier to use the well known y=mx+b substitute x and y with with your (x,y) ((1,3) in the first example) coordinate values, and substitute m (5) with your slope value and solve for b.

So 3=5(1)+b —> b=-2

Now rewrite y=mx+b with your b and m value so y=5x-2

ezpz

Thank you.

tbh the best i have seen on youtube <3

That’s why I love Parabola and equation of Circle.

OHH my Gosh is used to wrote backward equations.

Man suck at explaining things.

that’s really great teaching method , Ma’am i am from pakistan but i am really impressed by your teaching style,you teach very slowly by doing this i have cleared all point of this tiopic

hey, mm, it looks like she is too scared about something.

OK this is the thing, to overcome your fears, you need to be confident and free yourself because people are watching you live, so you need to practices that and anyway thank you for the lesson God bless you madam.

Dear Nancy, You’re beauty makes me strive to become a better math student. With every video, I fall more in love with you. Keep up the good work and keep making videos 😉

maybe you also want to make a video for our professors about “how to teach math CLEARLY to your students”

Thank you mam. U r soo beautiful.

Thanks

“not all heroes wear capes”

– metro boomin

metro boomin wants some more

@Zack Vasquez hahAha wow that was funny

She’s left handed and doing it backwards 😱

It’s mirrored. HAHAHAHA

@Christopher Jay Lazaro I realised after 🤣

@SONBON01 had a good laugh when I saw your comment lol. Can’t imagine how fascinated were you to think she really writes backwards with a left hand. Well, good luck with calculus. I still have a lot of nancypi videos to watch for my quiz later 😢

@Christopher Jay Lazaro Thank you , goodluck with you quiz 😊

Going to have finals tomorrow, finally I understood this topic, thank you for making these videos to help students

Thank you so much for your helpful explanation! I like how you took your time to fully go over everything.

I just want to see a 5 minute making of post showing us how you do the mirror writing trick.

eitughtueir she probably has a mirror that u could see through both sides and then placed her camera on one side and writes on the other just my guess

really in depth, but it was easy to follow and understand. In class, I was lost for a week when learning this topic, but after I watched this video, everything just clicked

thanks! 🙂

this is probably just me being a bit dumb but are you writing backwards?? i imagine theres a glass plane infront of you and for the camera to pic it up in the correct sense?? if thats the case what a badass ahaha,, thanks for the helpful videos :~)

OHHH i forgot editing software exists wow its just flipped around

Happy to say, your amazing Nancy Pi !

I like how you write. Reverse?

Hats off for your stle of writing😍😍😀😀

Smart women are sexy!!!

whaaaoooooo!!!! thank you, i’m really helped

I think it would be easier to represent sec(x) as cos(x)^-1 . So we have like f(x)=cos(x)^-2. And obviously we get the same slope 🙂

thank you so much

Finally a good one.

yeah, I mean the chick

Get lost idiot

Would it be wrong on the second problem to cancel x-1 on top and one of them on the bottom to get

-x/x-1?

Hi. I have a question. Is the equation wrote on the links section written correctly (x-x1=m(y-y1))? Thank you so much.

Thanks mam,

I like yr way to teach.

i love to watch your videos. not for the knowledge but for you only. you are very beautiful.

For the genius people who keep sayin ohh how can she write from right to left… actually she is writing from left to right the secret is on the camera she is reflecting her video so it seems like she is writing from right to left.

how you can do that ? writing from z to a ?

thank you for the videos!

Nancy, you’re everything I’d want my daughter to be!!!! You’re the best!!!

can u help me with Equation of secent line please

Basically, the secant line approaches the tangent as the difference in x values approaches 0. I explain more at

Speaking slowly nice

If only x is given and y is unknown, what shall we do then? Here (1,3) is given

I want to kiss you.

You made me love mathematics…

Can u pls use a darker color….pink is not easy to read ..thx!..

Thank you for sharing your beauty and brains ….you make learning a joy !

THANK YOU

You need to start wearing glasses. even if you dont need a prescription, you can pick some non scripts up at Walgreens. Get some cute ones.

why?

How would you graph that after finding the answer, do you have a video for that? Thank you, Nancy!

Basically, graph the parent function, and then use the points associated with the tangent line to graph the tangent. I explain more at

Luv❤️U!

Very helpful!

I’m trying my best to learn calculus with my last remaining brain cells. Thank you Nancy for this very comprehensive video.

Hey!! Very very thanks for helping me for my question which will help me to crack CBSE board exams.

Good

thank you. explained it perfectly in a way that I can understand easily.

Thank you my kween. I am forever grateful.

You are the best! I can only show love through subscription and likes 🤗

my teacher overcomplicated thee FUCK out of this, it’s so simple.

Thank you so much!

She bad lol.

wish you could do a more complicated problem.

Im in love with you

she is hot and beautiful

The basic Example really helped me get underway on my derivatives homework. I’ve never had to learn them until Uni, and still didn’t grasp it in the week I had lectures about it. Thanks for an awesome video.

so how do I find the equation of the tangent line:

f(x)=7e^−0.4x at x=7?

allah razı olsun şu güzelliğe bak

mam plx explain on the logorithm ALSO HOW TO FIND THE TANGENT LINE WITH THE HELP OF DERIVATIVE FORMULAS .

i love you

great…

At first i was confused how she was writing backwards but she must flip it in post lol

Very helpful thank you so much 😊

Thank You Nancy

If my maths teaches was pretty like you.. I’ll get an A for sure 😀

she teaches us happily

You won’t get a clearer explanation than Nancy P’s demo! Well done !

Thanks mam please video on the topic maxima and minima please💐💐💐💐💐💐💐💐

Thanks nancy

Mire ha mi eso es suma por motivo de un forma de hoyente

is she writing backwards?

Better than my actual college profesor

Gosh.. I am as dumb as a donkey. Actually donkeys are smarter than me, why am I even here?

I love you dear

thank you so much!! you’re my favorite youtube math tutor now!! please don’t stop using you’re platform to share and help the students like me who’s having a hard time understanding the lessons that are thought by our actual teachers. God bless you! xoxo

Right! Why is it hard for math teachers to explain things, but people on youtube can explain it so perfectly?!?!? I’m in a hybird calculus course and the online learning lessons is just screenshots from a textbook and doesn’t actually explain a lot of steps and why something was done. Then there’s examples of a lesson that was never taught how to solve. It’s just assumed I’m guessing. Then you have to pay another online website to complete class assignments……

Capitalistic america and lazy professors!

LOCD&LOOSE ugh, ikr 🙁

I don’t under the last part when you put 5x – 5? Where did the – 5 come from Nancy

Graceful.

how can you write in the opposite direction or is it some software which is doing this?

She’s just so good!. I could hire her for any amount

This was extremely helpful. I didn’t even need to watch the full video. Thank you for explaining it thoroughly!

She’s like Meagan Fox, but intelligent.❤️❤️❤️❤️🌹🌹🌹

I bet you got 750 out of 800 in your Math Sat

does she have to write backwards for it to not look flipped for the camera?

Visual ASMR.

How does she draw everything backwards

I’m certain she flipped the video. I was wondering the same thing!

ily ty

Thanks a lot, NancyPi. As always, you make Calculus easy to understand.

you’re pretty……………….smart! haha

علي الصديق الاسطوره

If you were my teacher, wow, there’s no way I’d be able to concentrate on math. I know you must get that all the time. Have you ever noticed that you’re actually a very beautiful woman? Sorry! LOL

Suddenly, I am this much more interested in math.

She’s hot no cap now I wish she was my calc teacher

god bless you for not littering your board with d/dx’s and stuff.. like obviously we know whats going on you dont need to make it look so messy

This was extremely helpful! Thank you!

Thanks that simplified a lot!

is she writing backwards??? how is this video possible??? im so confused

Thanks

Very helpful

a linear…..line 🤣😂😅. Great video. I’m learning so much calculus. I don’t even know why. I’m not even in school!

I swear, I you were my professor, I would fail your class! ‘Cause I wouldn’t be able to keep my eyes off you!

I love how she speaks slowly and gives multiple examples. It’s almost like she knows I’m a moron and yet she does not judge me.

A true teacher. 😂

shes judging u silently

HAHAHHAHA hilarious comment

I feel you bro

I really appreciate how you explain each step and include the simplest of things like labeling the slope as ‘m’ because some of us get confused when only slope is said.

There is a special place in heaven for you madam – many thanks!

you say the third step is to find the y coordinate yet because you decided to already include it in this example you just skip over it. Would have been nice to see that step in case a problem doesn’t give the whole point.

Really! Thank you!

First you use the left hand, write in the opposite site and you do calculus so you are way to smart.

Thank you for doing these. You are an awesome teacher. I wish I had these videos when I was taking math classes in college.

you lost me at “find”

she is so pretty

Can you make a video specifically on subtangent

Thanks for the explanation

When you mistake “at” for “a+”.

Thank you queen

saved thank god–

Hi mam

Hi guys, am Nancy

She does too much for her to just ask for a like OR to subscribe. For her work she should always say to like AND subscribe. Love the material she puts out!

I find it difficult to see when u use pink colors……

10:13, f(2) = 1

Madam, all your lectures are so lucid! We did not have calculus in high school, and as a clinician I needed to understand the dynamics of the on-going Covid-19 pandemic. I have been able to learn calculus from your lectures, and have been successful in understanding the epidemic curves much better. thanks so much!

Brain: look at the way she solving

Heart: look at her beauty

where are you when I was Yung!!! awesome illustrative from an awesome girl

Very helpful mam

Hi

Do you do one on one math tutoring?

🥰🥰🥰🥰💞💞💋

Thank u soooo much, ur videos are life saving !!!

you r a great teache

“it’s a linear line”

So so helpful! Thank you!

prof has a great saying for quotiant rule, ” low dhigh less high d low, down below, low square we’ll go.

i lost

How does she write backwards on the board so perfectly?

she writes backward

Did anyone else notice see only brought square root 3 over and not sqr root 3/2. Or did I miss something?

Disregard my previous comment. I had a slight senior moment.

Omg if she was my maths teacher I’ll be present in the class every day

This is so Dope

How’s she writing backwards doe

Dude, she wrote backwards the whole time.

Great job. Please I would like to know the devices you used in your lecture that made you to face viewers all through your lecture.

I would appreciate if anyone can help answer my question

verry good math-teacher !!!

Soooo much more help than my professors or the online learning tool. Found how I am going to learn calc this semester. Any suggestions for Orgo I?

Do anyone ever wonder how she can write inversely

These are very helpful, just a note, pink is very hard to read.

Hi ma’am

I must say commendable video.

Love from India 💖

By the way,Which board are you using. Where can we buy one.

You seem really good at reverse writing. Nice skill.

0:24 It’s a linear…..line

Thank you. You really helped.

THANK YOU SM you just saved my grade

beautiful, simple, to the point. Thanks

Very good teacher! Thank you nancy!

NANCY IS KINDA HOT LOL

Is one the only number that starts with w? are there any other words written with the letter o that sound like w this is driving me nuts help me out Nancy

thanks for the method and different examples

clear explanation

Ahaaa an MIT graduate … that’s why 😀

Are you writing on a screen? on a window??

When I see such a beauty woman I can’t think about anything except this woman (

VERY NICE #STUDYMATHESILY

You are a great teacher thank you and bless you!!!

wow she writes everything backwards so nicely