2.1 Finding the Slope of a Tangent Line - Example 1

[@Nhxn_]

Here is the shortcut to do this: Step 1: Find the derivative of x²+1 Step 2: The Derivative is 2x Step 3: Plug X=3 into 2x, which would look like 2(3), and the answer will still be 6. Doing this will save a lot of time.

[@ppan3]

he's making use of the power rule, guys.

[@zadie_9599]

Kanye East thank you because this was much much simpler

[@sparty5807]

7 years later and ur still a legend my dude

[@truth517]

Thx!

[@Nhxn_]

time flies, you are all welcome!

[@anaiyalate1441]

I can't even properly express how helpful this was to me, thank you so much!!!

[@YaoiFan22]

I agree, though this may not fully help me with Calc and Precalc I'm less likely to fail the class again this Fall Semester.

[@HarryMonn]

very useful 12 years later thanks mate

[@withthebest7029]

I was actually crying out of frustration before I found this video. Thank you!

[@wolframalpha8634]

This guy is amazing!!

[@jhnadek]

@@wolframalpha8634 ikr

[@eurofusioncuisine6994]

This is the only video that I've watched that actually helped me out.

[@rootmath]

I'm really happy it helped you!

[@wildfirestudios4868]

Me before watching this video (2:10)

[@UzsDc1UZ]

Bruh I'm done 😂

[@yuju1195]

Same 😂

[@hilaryshapiro5654]

Wildfire Studios me after watching this video

[@dmyjshy]

from several years ago, yet still the only video on youtube that helped in the slightest

[@ishansaxena4653]

Google recommended me this video. Needless to say it definitely helped.

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@PBUH03]

your simplicity and patience while teaching is admirable thank you for this lesson

[@liamjudd8166]

wtf is a derivative

[@richardadamwais9734]

i always confuse it but you really clearfied me thanks from djibouti

[@RicoNuko]

You can just solve without the numbers and do: (f(x+h) - f(x))/h = (x^2+2xh+h^2+1) - (x^2+1) = (2xh+h^2)/h = h(2x+h)/h =2x+h lim (h -> 0) = 2x + 0 = 2x *At that point you can just plug in the value (3) = 6.

[@ryliebulan6093]

For any more complicated expressions, you may use L'hopitals rule, derive, and then plug in the value of x to find the slope of the tangent line

[@Fabiangarcia101]

RootMath, you're the real MVP!!!!

[@NIGHT2K17]

Great explanation, I was forgetting to substitute the f(3) into its own function as well.

[@akshajdev7342]

Thank you so much man ,I have been struggling to figure out about differentiation, your video helped so much:)

[@mohammedyousef4005]

Where did the six come from and why was there a new h?

[@laurencrom]

You should post some questions to work on after completing the video. That would be super helpful! Thanks.

[@ErrorLoading404]

It's both a shame and awesome that a 6 minute video can be so much more informative than a 70 minute lecture

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍💐

[@thelearningcentre]

your patience while teaching is amazing may ALLAH bless u

[@JoshuaVoss]

He made this video in the morning, because you can hear the birds chirping at the end of the video :)

[@sherry3501]

awesome video. thanks!

[@cortiz8726]

can someone help me i dont know where the 6 came from when it was 9h +6h 3:15

[@jjalfaro2205]

same

[@rootmath]

Expand (3 + h)^2. You get (3+h)(3+h) = 9 + 3h +3h + h^2 Add the two 3h terms to get 6h

[@cortiz8726]

@@rootmath ohhhhh thank you very much

[@hhunter872]

Dude, I can't thank you enough for making this. My gr12 functions teacher is so bad, and this helped me understand.

[@smiles4u92]

Thank you sooo much for this video!! You broke it down sooo well!! God bless you!!😊

[@incognito979]

May the FSM bless you for your kindness.

[@YourProfessionalSquare]

Thanks I'm taking a five week mini course and this helped a lot

[@jonathanhardy9747]

This was really helpful, but how would you apply it to f(x)=x^3-3x^2+8x where x=2

[@Ms7peaches]

Thanks this video helped me a lot. Much better than seein it in class!

[@mg3_the_mix741]

Does anyone know how he got 6h in the equation of distributing? that just kinda threw me off

[@sneakypress]

See comment above, by NN .

[@markliu22]

this video is so good i want to give you money

[@rootmath]

Well if you have a lot of money and want to make a donation to rootmath you can. ;) I'm glad this video helped you!

[@Foxers666]

Question; what kinda laptop / computer you using to write this on? Also great video!

[@Else-v9h]

Thank u for understand this topic, your the best 💗✨️

[@sidekickxx]

Im sorry, when you expanded the first term, where did you get 6h from?

[@just_there5427]

Factoring (3+h)^2 gives you 3(3) + 3h + 3h+ h(h), which is simplified to 9+6h+h^2

[@deemckinney1238]

Great example and very nice, step by step!

[@HailieB2468]

this was really helpful for finals review!!!!

[@PierrosGarage]

Wish my teacher posted videos like this!

[@grantemery6152]

lol exponent doesnt look like it wants to be there

[@Nhxn_]

This is late, but it came from foiling (3+h)², and once you broke it down it would look like (3+h)(3+h) and then you foil it.

[@sneakypress]

Thanks NN., that’s what I was looking for. 😉

[@amyangel9268]

This was spectacular! Thank you!

[@yuju1195]

Thank you so much this has been super helpful!!

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@rosmahanihamid6023]

oh my god this video really help me. thank you so much.

[@warrengregulator]

Thank you very much!! Very well explained.

[@chrisfreedman6977]

I dont know why you wouldnt just do f '(x)= 2x and then just plug in the 3

[@sofiavaldez3020]

I think because that would just give you the y-value, not the slope. So x would be 3 and when you plug it in, and get 6, which would be the y-value. So now you found the coordinates of the point (3,6)

[@rootmath]

chris freedman that certainly would be easier but this video is meant to help finding the derivative of a function by using the definition (instead of using the power rule).

[@gregl2249]

rootmath but if u use the power rule---u still have to add on the 1-----(2(3)+1) would be the new equation---=7 instead of 6 ?????? could u pls explain?

[@r.gutierrez5070]

+greg l That is because the f'(1)=0 so after you get f'(x^2+1) = 2x there fore f(3) = 6

[@fizzyjizzz]

Couldnt you just turn it into derivative form? So thats x^2 + 1 = 2x + 0. And at x = 3 : 2 x (3) + 0 = 6?

[@gregl2249]

fizzyjizzz where can i learn this way?

[@scottmenace1]

fizzyjizzz that depends on your teacher, our teacher require us to derive it by using definition of derivative

[@MyEagleeye1]

Thanx a lot, u hv made it so easy for me

[@user-bw8dv5hc8l]

3:17 how did he get 6h ?

[@FighterDyte]

Wait where does 9 + 6h + h² come from...Aw screw it I tried. Im just going to wing my test tomorrow xD thanks for the help though.

[@co_okie]

@Ammeer JT lmfao

[@Addicus_brown]

Wow, you’re amazing. Thank you

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍💐

[@jadendw1234]

How do you find the slope without a function and only a given point?

[@Ironwoman92]

ok... I just started on this unit, but why do they call it tangent line? I don't see any tan/cot function inputs?

[@IxBlind]

+Sith Lord Its Called Tangent Line because the Slope of the Line "Touches" the Parabola or said Graphed Equation. (The Word Tangent is derived from the Latin Word "Tangens" which means "Touching")

[@IxBlind]

y = x^2 + 5x When x = 4 Is the Slope 13 or 9?????

[@joeverzino]

+Ix Blind 2x+5=8+5=13.

[@gamesxotics4712]

How do you know how long the tangent line is?

[@mattstewart4980]

You sir, are a genius!!! :D

[@curias7]

what tools(software) you are using?

[@paigegrey9379]

what if the value of x is not given?

[@hammyhamham945]

okay but what does the 6 mean???? is that the y-value when x is 3???

[@dylanlandeau4390]

6 represents the slope of the tangent line

[@nuggeteater69]

the y value when x is 3 would be (3)^2 + 1, so 10.

[@gregl2249]

Fantastic ---thank u Sir!

[@Nohaii6]

Thank you so much , now I understand 😭😭😭♥️♥️♥️

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@khalidshare5842]

i know this is a stupid question but i'm lost on [(3+h)2+1] become 9 + 6h + h2 + 1?

[@Kassiemg12]

khalid share haha thanks I thought I was crazy too

[@Noon-ln5jk]

khalid share (a+b)^2=a^2+2ab+b^2

[@MiiMaker]

@N "or FOIL it!"

[@the-engineer-Delmont]

Thank you, And Thank you again.

[@letuslearnscience-piyushku284]

Nicely explained

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@gingermavy]

Thanks. A confusing subject.

[@alexogungbangbe9190]

how did he get the six

[@priyapitre4468]

You saved me from failing Physics

[@rashidghaosi2337]

thanks! this was very helpful!

[@CrowAndBar]

can anyone help me... Find Points of intersection of the function y=x^3-3x^2+2x of the axes , i have no clue how to do this , i moved from a 4 point class to 5 point class in israel , and this makes no sense to me

[@Omar-zn2qo]

Whats the point of writing the limiy?

[@heresjohnny7867]

where does the 6h come from?

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@sneakypress]

Nice photo 😂. ( 3 + h )^2 = ( 3 + h ) ( 3 + h ) = 9 + 3h + 3h + h^2 = 9 + 6h + h^2 . I think it’s called factorising ? 🤯

[@sexybeckygurl95]

Very helpful, Thanks

[@cipherbenchmarks]

Where u get 6h

[@markanthonyignacio3528]

what is the of the slope tangent line at the given: y=1׳; at (2,-7) i need help po what is the answer related architect salamat sa makakasagot

[@gamesxotics4712]

how did u get 6h

[@johnathan252]

this is slow jsut find the derivative of x^2 + 1 then plug in 3 and u get 6 u can do it in 5 secs instead of wasting time

[@RealProfessionalPotato]

Thank you Kind sir

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍💐

[@Nhxn_]

It's been a while since I've done trig, but most likely yes.

[@tiffanyesola1917]

so helpful!!

[@shyanncookie3306]

Where does the 6h come from 😭

[@zahrashukri4436]

Thank youuuuuu

[@ExecuteOrder420]

you should of used the shortcut the derivative of x^2+1 when x=3 then you get 2x then plug in 2(3)=6 much easier

[@bradyb4208]

yes, but this is a proof why that power rule works. You got to understand where the equation youre talking about comes from

[@gregl2249]

Brady Bower spoken like a true Math instructor-ha

[@Soccerloveandpeace95]

thank you so much !

[@computingforlife3426]

thank you so much

[@stobiguglrekao4683]

The slope is 6 what? What 6? WHat oes that mean?

[@guantamanera]

Yeah, show them the hardwar. Dr Sylvanus P.Thompson wrote on the prologue of his book: ``Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics - and they are mostly clever fools - seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.''

[@katherinel8970]

so neat!

[@khurramkhan8118]

love u man love u

[@jessesolis8409]

Way more complicated than it needs to be.

[@speedspeed121]

Considering this is the first step in learning derivatives, I think it was well produced. People need to visualize a derivative before they move on to the rules.

[@juliadever7899]

savior

[@sabrinayock3137]

thank u!

[@David-uu7nl]

I feel dumb this is so easy, yet i had trouble ;p

[@cloudspace8483]

what is h

[@Ian-Threaded]

thanks

[@SaladFarsi]

Cmmon man u dn't need to waste 6 mins to get that derivative u can ezly calculate the slope jst like this f'(x)=2 (3)=6 so m=6

[@canadianiam]

no shit dumb ass lol

[@VictoOor2004KSA]

@eyelykeicecream and me its very easy

[@alpsenel]

LOL :dddddd 2:11 ROFL OMGG I LAUGHED SO MUCH

[@jenniferl6212]

same haha

[@littlespoon7942]

I didn't learn to do it like this :/

[@openyard]

What! Are the videos from 5 years ago really helpful? Yes, they are 😅

[@AsianDiva69]

So why aren't you my teacher ..?

[@fruitpenguin6285]

HOT 10/10

[@beoptimistic5853]

https: //kzbin.info/www/bejne/fYSpiad-npeYgJY👍👍👍👍👍👍👍👍👍👍👍👍👍👍💐

[@YorumiTech]

agree

[@jadezares]

Be my teacher.