Finding the Equation of a Tangent Line

[Shadowcommand]

Thx for the Formula, all I needed to know =)

[philster00700]

I remember doing this stuff in grade 12, it seems so simple now.

[thenebbishroute]

I love your tutorials. Even if I am getting the answers in my homework correct, it's nice to hear your voice and review your methods for problem solving. It gives me confidence I am doing the right thing.

[yourdailycydiafix]

Thanks SOOO much! You explain it 1000x better than my book

[Munezfan30]

Is this where everyone goes before your final?

[patrickJMT]

@Munezfan30 some people at least :)

[princessgaga7]

thank god for youtube!!!

[AliveDog]

wtf did people do pre-youtube?

[patrickJMT]

@AliveDog i used books ; )

[Hardy123Zhao]

@patrickJMT what are books? O.o

[Rondo205349]

Can i please have your email address patrick. Im a college student and i have an important calculus question that ive been trying to solve for a day now.

[patrickJMT]

@Rondo205349 ha, you would have to take a number. yours would say: #41,456,339. the sign would say: now serving #1

[TheSahar58]

Hi. Great videos!

Are all tangent lines linear? Is there any e.g. sigmoidal tangent line?

[11Dykema]

Seriously this is helping me review so well, great video and great explanations

[patrickJMT]

@11Dykema glad i could help : )

[asdfgh1880]

Awesome vid, I need this. Good work!

[awsomemills123]

My exam is in 5 hours thank you for the last minute study help!!!

[iluvishreddish]

you are amazing! <3 can you be mine? lol jk

[cylee0610]

How come there're dislikes? Great video!

[jo047c]

Started studying for my Calc I final by watching your videos. Thank you so so much for helping me pass that class :') I know you don't have to post these videos for free on here, but you do, and for that I and so many others will be eternally grateful!

[patrickJMT]

@jo047c glad your class turned out ok : )

[kickit246]

Hey I doubt you remember me PatrickJMT, but I was really bummed out as an impending final was about to be upon me. Anyway, I just checked my grade AND I PASSED!!! C+ (All I wanted...). Thank you so much for being here. I was having nightmares about this course.

[patrickJMT]

@kickit246 glad u passed the course : ) only sweet dreams now!

[LongbowApache96]

@ahmed735788 So do I. Good luck.

[ahmed735788]

Tmwr I hv math exam n I'm studing from ur channel .. Let's see the result :) .....

[Moudizg]

I LOVE YOU <3

[LivinOnDaMusic]

just FYI you have helped me so many times i think youve earned a free ticket to heaven...no....i KNOW youve earned a free ticket to heaven!!! <3

[chrisfellable]

excellent video, had to do this for an exponential equation, tougher maths, but this basic stuff actually made it really easy, thanks a lot

[toan17]

I've been watching ur videos since 2010 ! 2mr i have final, and thank for doing ur best to help the students out there !!

[patrickJMT]

@toan17 happy to help : )

[thesinnerheloves]

I love math too!!!

[TheVegetarianPro]

I came here my first time a few weeks ago saying "Just this one time" but here I am... multiple visits later... getting ahead of my calculus teacher  and i give up; You sir, have a new subscriber

[jchen0011]

i learned more from this one video than i did in 3 months of calculus class

[patrickJMT]

@jchen0011 come back and watch some more then : ) 

[mcfearless666]

Is that y-y1 thing just the same as y-b=m(x-a)???

otherwise:

PATRICK YOU ARE GOD.

[TheHande4]

Patrick, do we use the quotient rule only when there is fraction? Can't we use it when there a normal eqution like: y=4x^5 + 6 ?

[T3N0RI0]

@TheHande4 yes, that is why it's called quotient rules. for y=4x^5+6 you use the sum rule. which simply is to take the derivative of 4x^5 then take the derivative of 6 and add them

[ilovephysics1122]

very clear explanation.

[punksoldier33]

Do you have a video that shows how to find the equation of a line that goes through a certain point and cuts off the maximum area possible of the first quadrant?

[90blueg]

is anyone taking ap calculus ab and would like to help out someone who doesn't get it? pleasse really having trouble with it but dont want to quit thanks

[ChronoTriggerMusic]

This is difficult to masturbate to.

[Luckyxseven]

@ChronoTriggerMusic im masterbating to this just fine.

[learnspanish23]

thanx really helpful

[chankom]

thank you!

[goliibandari91]

helpfull :D thanQ !!

[MrStupidmonkeyboy]

i've tried and tried and i still don't understand... at the end of equation number 1, what made you add that 4?

[UltimateSAB]

thank you!!!! you are one genius!!! you helped me so much!

[OTEP1234567891011]

I used to think that god didn't exist, but now I know he does: PartickJMT...nehh, god's still not real, but you're definitely god-like. :)

[tahaali3]

i wish if could be just like you are amazing , thank you

[fm269309]

Do you have any videos regarding recursions? My calc 1 class is geared towards biology majors and we use recursions related to bacterial population growth over time.

[chippy506]

man i'm doing this for A levels(grade 11) why can't we do this in uni like all the other countrys?

[dinotles]

@chippy506 You are probably in some genius class and noone has told you yet

[chippy506]

@dinotles lmao maybe :( nah i suck at school :P

[oioioioioioikjkjkj]

you are the best

[Lateilla]

I dont really understand how you get tan(π/4) = 1 and 1/cos^2(π/4) = 1/(√2/2)^2 are there some rules that would give us these results? or if i do it on a calculator it will produce the same results?

[patrickJMT]

@Lateilla yes, a calculator does the same. you may look over the unit circle and evaluating trig functions

[patrickJMT]

@Lateilla Evaluating Trigonometric Functions at Important Angles, Ex 1 <---- check out this video and the second one as well. it may help

[Lateilla]

@patrickJMT thanks! :)

[naturada137]

@Lateilla

Trigonometric functions work on the basis of a triangle. Do you remember SOHCAHTOA? That's basically what it is, but it's on something called a unit circle, which has angles. I'm sure he's probably got a video on trigonometry somewhere so go check it out.

[MissLovely377]

i have a test tomorrow and i really hope i do good because these videos really help, thank you!

BTW why don't you do tutoring anymore? cuz i think a bunch of people might have hw questions that confuse the shizz out of them

[ioioi210]

You, sir, are a helpful person.

[patrickJMT]

@ioioi210 i try : )

[abbz39]

THANK YOU SOOOOOOOO MUCH !!! much better than my professor.. Do you have a curve sketching video ?

[patrickJMT]

@abbz39 yup. there are calculus playlists (although some stuff is missing) on my channel page. you may check out the calc 1 playlist, or do a search of ' curve sketching '

[InfernalChaos77]

why can't my professors teach more like you...

[MetallicaSlayer21]

I truly don't get it. It seems that not only me, but every other commenter finds this much easier than what the teacher teaches. Do the teachers sign a contract that states they have to confuse the hell out of students?

[patrickJMT]

@MetallicaSlayer21 yes, that is what they do.

[Astronaut585]

this is so much clearer then my middle eastern teacher's rapid spew of numbers. thanks

[33jalapeno]

THANK YOU!!! These videos are the only hope i have of passing my calc 1 midterm tomorrow morning!!

[iampeetz]

It takes calculus and translates it into English.

English is my worst subject :(

[KayferProductions]

Guys this guy is great but let me make a point. Whatever he taught is from your book (not mentioning the teacher). You can learn the same from the book, if it wasn't possible the college district wouldn't approve the book for colleges to use. You are here because you know you'll learn the same thing in 10 minutes, instead of reading the book (boring) or listening your teacher for 2 3 hours (even more boring)

[Pretoriafly]

@KayferProductions: I totally agree. Read all the [important] chapters, and be sure you completely understand it to pass any exam the teacher will throw at you, but alas our attention-spans are too short for that. :P

[KayferProductions]

@Pretoriafly agree agree

[lucuador1992]

wow.....just wow. You made this SO easy! My teacher wants to make this so difficult for us -__- I really can just stay at my dorm and watch your videos than go to class! Thanks so much :D

[xIzaac94x]

This is so much easier to understand than my teachers ramblings. I'm gunna watch all these before my HSC, should help alot, Thanks!

[patrickJMT]

@xIzaac94x no problem, come visit any time : )

[Valoredxl]

Thank you for posting all the videos. It takes math and puts it into english. I don't even bother with the textbook anymore, just find your video on the topic. Thanks a bunch!

[patrickJMT]

@Valoredxl my pleasure ; )

[ProjectAwesome1]

hey my math prof is an asshole: care to help me with evaluating the derivative of e^(e^(3x+3)) at x=0? every time I put this into a derivative program i get an expression I cannot evaluate...

[nygiants595]

Thank you, this is helping me a lot with my Engineering Calculus class

[231Easy]

How do you find the equation of the tangents to the curve y=sin x at x= -(pi), 0 and 3(pi)/2 and Graph the curve on the interval [- 3(pi)/2 , 2(pi)] . PLEASEEE HELP

[mhyde177]

YOU ARE THE ONLY REASON I AM GOING TO PASS MATH 140 IN COLLEGE

[patrickJMT]

@mhyde177 happy i can help you out : )

[edre44]

HOLY SHIT! AWESOME!

[jasonhan8733]

lol at the beginning. LOVE MATH! ME TOO xD lol

[EXOisEspy]

Sorry to bother you, I saw one of your videos on it, but I need help on one specific problem.

It's asking me: Find the slope of the tangent to the curve y= 3 + 4x^2 + 2x^3 where x=a.

For that, I got 8x-6x^2.

But then the next question asks me: Find equations of the tangent lines at the points (1,5) and (2,3).

I'm stumped :(

[XVD98A]

How would you find the equation of a tangent line given the equation of the circle (x^2+y^2=100), parallel to another equation (same slope I know), and given the fact it has a negative y-intercept?

[patrickJMT]

@XVD98A you'd have to use implicit differentiation to find the derivative, and then set that equal to the desired slope

[jackyng008]

@XVD98A i will use the tangent property. it is perpendicular to the radius.

let slope of radius be r ,slope of tangent be R r=-1/R (R given)

the center of circle: (0,0) (by(-D/2,-E/2)) then find the equation of radius sub. it into circle equation

you should find two point

sub. it into point-slope form to find the equation of tangent. confirm the true one by using those y-intercept.

[mjsather2000]

it is so much easier to just listen to you talk for 5 minutes than listen to my teacher talk for an hour and a half... i learn so much more

[aa7xcc]

you are simply amazing patrickjmt :)i passed my precalculus class because of ur help. n this semester im gonna do the same with my calc class.

[ladymanladyful]

my god, i have never meant thank you as much as i do now

[patrickJMT]

@ladymanladyful ha, come back whenever you need a bit of help : )

[SLIMmcGlinn]

Thank you Professor Patrick!

[snugglebear97653]

i hate calculus to the ^10 power ....

[jojogirl2008]

Thank you so much! I am so grateful for u and ur videos! :)

[Connorkey101011]

Your the man

[DoomDude20101]

Awesome tut

[Cockdonut]

English is my second language and thanks to you I now understand math in it. :)

[meganengler93]

You are the man! Can you please be my Professor?!?! Your videos are so helpful and you make it so I can actually understand !

[shadowlink1992]

Thanks alot.

[ksroot13]

This was so helpful it really helped going through it step by step thank youuuuu

[MrBamSquared]

How can you find the tangent line of line with radical denominator? forgot what it's called. xD

[AzarHakim]

I love you.

I love you.

I love you.

I love you.

Please make a Calculus CD or book , i would gladly buy it.

If i get an A on my test, Im donating $20. They should've had your youtube channel as our textbook instead of the bullshit $100 book they make us buy

[patrickJMT]

@AzarHakim ha : )

[ARayaOfSunshine]

Ah, reviewing this stuff from last year, it's amazing how much I can forget in one summer. Thanks a lot, patrickJMT! You're a total lifesaver!

[hkt111791]

I don't get the 2nd line of finding f'(x) on the 2nd example. What rule are you using? I'm confused ! Would anyone can explain for me about that part ?!

By the way, nice video :)

[ki11uah]

so why is f'(x) = 2x ? help please

[hkt111791]

@ki11uah u take down the square of the x down, so u have f'(x) = 2x. That's one of the rules to find derivatives

[ARayaOfSunshine]

@ki11uah for f(x) = x^2 the shortcut way is to bring the exponent to the front and make it a coefficient, while subtracting one from the exponent in the process. That brings you to f'(x)=2x because the 2 was brought in front and 2-1 makes 1, the exponent.

[jamesr169]

@ARayaOfSunshine

[snx3gs]

this is like math porn for my head!!! THANK YOU!

[bgrab69]

I dislike this because I dislike math. Doing AP Calc BC this year, anyway.

[TheNumber2Pencil546]

is there a difference between finding the normal line and the tangent line?

[patrickJMT]

@TheNumber2Pencil546 yes, a normal line is perpendicular to the tangent line.

[griggles517]

you saved my life.

[oyetligaya]

can someone solve this please.. a^3 - x^3 at point (a,0) where a is constant....

[kiras771]

can you graph all the examples plss..

[Gotfryd1590]

@patrickJMT

if I had to find the Equation of a Tangent Line but had two variables would I use implicit differentiation and use y' as my slope?

[NIGBEATS]

Patrick, If I get an A on my final and an overall B in my calc 2 class, I am going to send you one hundred dollars...no joke.lol

[tamnguyen411]

how you got next step with F(x)=2x/(x+1);(1,1)

[kenniconnieamy]

Can you please make a video for how to find the unit tangent vector?

[ipkyoudown]

hey tan(pie divided by 4) is 0.0137........ not 1

[TheSingerwannabe1]

@ipkyoudown actually using the unit circle you can go to pie/4 and see that sin(pi/4) = sqrt 2/ 2 and cos(pi/4)= sqrt 2/2. Recall tanx=sinx/cosx, therefore sqrt 2/2 divided by sqrt 2/2 will equal 1. If you have evaluated in your calculator, make sure to switch to radians.

[RoundHouseRecords]

pointless math

[tanginumin00]

i have a final tmrw and i feel like watching all your videos just in case lol..

[cdvitek1]

thanks dude, this helped alot

[lxdannydxl100]

How would one convert from the secant line to the tangent line?

[GrandMasterJuan]

so thats why that point slope was important ....

[TheMajorpickle01]

wow, ive had the gradient y values x values, ive been staring at a markscheme for 30 mins and all i had to remember was one tiny equasion? wow

[bhardwajankit42]

U r truly a best teacher on this planet!!

[EveningCommisioner]

for everyone who doesnt know he used the power rule to find the derivative

[khwezi1986]

so the 13 people thwt do not like this video whats their problem

[Nirvana32058]

Damn you saved me from one question from the AP Calc Test. Thanks

[angryrantingguy]

YOU FUCKING IDIOT! EVERYONE KNOWS HOW TO MULTIPLY 2 BY FUCKING 2 BUT WHAT WE DON'T KNOW IS HOW TO FIND THE FUCKING DERIVATIVE!!!!!

[zakariyya90]

@angryrantingguy dont you know how to differentiate? jus mutiply the number by the power and then decrease the power by one. so y=x^2 will become y'=2x tada! and once you got your derivative then subsitute the x value you have in order to find the gradient which you put back into the equation of a line!

[CaNaDiiAnBaCoN]

@angryrantingguy when watch his derivative videos.....

[LlamasEatHotdogs]

@angryrantingguy why are you watching a calculus video if you dont know how to take the derivative? gtfo

[charles125]

The first formula you posted is all I needed thank you! I saw it being used in my textbook and I had not seen it before. But with only a couple seconds here I see it's an actually formula.

Thanks!

[hackinU4lyf]

wow, honestly you are great help, these videos of calculous that you provided have helped me throughout my entire calc class, i don't even feel like going to my classes... lol thanks man

[Superdanger2]

thanks, this is helpful

[metalraider187]

F(x)= position

F'(X)= Velocity

F"(X)= Acceleration

F'''(X)= Jerk

F""(X)= Fuck if i know lol

[space1patrick]

@metalraider187 snap. crackle, and pop are the 3 after jerk :D

[FallenStar117]

@metalraider187

wrong notation bro

[anonaccount77]

Where did you get "y"? in (2,4)

[bizkitfan49]

@anonaccount77 (2,4) is already on the slope of x^2

He just wants to find the tangent line connecting to x^2

[mrvinceeee]

Thanks, very helpful :)

[TheKoumbare]

@ARQ911 The derivative is the slope of the tangent line.

[Kioliab]

thanks man, i have a calculus test tommorow and you just made an entire quarter's worth of classes make sense. you're awesome.

[dajakesta1234]

then wut is with the y2-y1/x2-x1??

[crazykillah72]

hey thanx a shitload man, these videos are so descriptive and precise honeslty thanx =)

just an exploration question, what would happen if instead of evaluating at f(x) u evaluate at f(y), would u get horizontal tanent line?

[DemonPacman]

You're doing a great thing for the community by putting these videos on youtube.

[Addicted2Boners]

This video made my wiener get hard and stand up which is causing me to get alot of dirty looks in the library :(

[garyau1994]

i thought to get the tangent slope you take y2-y1/x2-x1 how did you get 4? i thought it as suppose to be -1/2??? maybe im at the wrong vid or something :S

[Wilsonaire]

@garyau1994 y2-y1/x2-x1 will get you the slope of a line, but not the slope of a tangent line. You need to take the derivative of f(x) to find the slope of a tangent line. You may be at the wrong vid if you aren't in calculus.

[Scotty0390]

This is awesome!

[patrickJMT]

@ARQ911 what is the derivative? what does it represent/ stand for/ mean?

[pillarsofcreation1]

Ahhhh, thank you sooooo much!

[CrazyMickey21693]

Umm, I visited your website for finding the tangent in Implicit and stuff- could you perhaps clarify which one its under? Other than that I should let you know that me and almost sixty other girls study all the time from your videos because our teacher is... unhelpful in class so really, God bless you xx

[pejared]

Oh my gosh! thank you sooo much! you make much more sense than my calc professor.

[pejared]

Oh my gosh! thank you sooo much! you make much more sense than my calc professor.

[MsMiyu12]

thank u so much!!!!!!!!!!!!!!

[Bravo27nc]

Pretty neat handwriting for a lefty. Good job presenting the four problems. I appreciate the courtesy

[ghotra2010]

when you got the derivative of the function, did you multiple by substituting in the derivative which was 2 into the equation of the function to get 4?

[brendasoto11]

how about y=2xcosx ?

[rashaine]

I live in jamaica and calculus is abit hard for me so im really glad i have been able to learn more easily through your videos

[rashaine]

I live in jamaia and calculue is abit hard for me so im really glad i have been able to learn more easily through your videos

[RandytheAsian]

thank you i've been getting destroyed in calc 2 because i forgot how to do this haha

[bkmendoza]

perfecttt...!!!! thanks a lottttt!

[1MMcN]

Outstanding! you earned each view on this video! thanks p.JMT

[burnside510]

Great job! makes perfect sense.. just always obey the rules!

[demnmn]

hmm can you help me find the derivative of this equation y=2x^3-5x .... im stuck somehow in 2h^3-10x+5h/h.... without it i can't find the equation of the tangent line at point (-1,3)

[BumChikaWaaWaa143]

Your videos are awesome O_O

I wish you were my calc teacher for my class :D !

[jvrcb17]

Hello patricJMT,

I really enjoy your videos since they have helped me view and understand calculus from a different point of view. I have a request for a tutorial. This is the only section I am completely stuck in and I have found no help online. Would you be able to post a video about Instantaneous Rate of Change? I would really appreciate it.