Differentiation from 1st Principles | Calculus by ExamSolutions

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In this video on differential calculus I show you how to do differentiation from 1st principles. Differentiation is used in calculus as a measure of the rate of change or gradient of a function at any general point. The notation we use can be dy/dx to signify the first differential of y=f(x).
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Опубликовано:

17 авг 2011

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Комментарии : 154

@pleasework96 10 лет назад

This is the simplest explanation on the whole of youtube... trust me i know

@jasontscooke 5 лет назад

just done the same tour totally agreed

@CJ-ow4hd 4 года назад

haha!

@martinconnell7939 3 года назад

Nice comment. Happy new year for 2021

@robertbrodie9566 5 лет назад

You just taught me in 14 mins what my maths teacher couldn't in 1 hour

@hoi288 9 лет назад

These explanations are really good, because you explain the method in a very simple way whereas others just draw a graph and point at it. Thank you so much!

@ExamSolutions_Maths 9 лет назад

You're welcome

@raimsa4081 9 лет назад

***** lol maybe we have the same lecture "draw a grah and just point at it" hahaha

@ioft8542 2 года назад

you're welcome

@faruzsyed 6 лет назад

i dont think anyone has ever explained the first principle better than this gentleman . Its compact enough and yet comprehensive. Many thanks!!

@callummatchett8937 10 лет назад

I like how he writes the letter ' f '

@Almilany95 12 лет назад

English is my second language, but i can understand every word you say!!!!!! And its so rare for me to find an educational video thats so easy to understand but so useful THANK YOU

@ExamSolutions_Maths 12 лет назад

There are two terms in 4h + h^2, the 4h and h^2. So you must divide each term by h not just one term. Try it with numbers. (4+6) / 2 does not equal 2 + 6 or 4+3. Dividing each term by 2 gives 2 + 3 = 5 the correct answer. Hope that helps.

@sleepyyymoon 9 лет назад

This is very clear, thank you, your videos are lifesavers :)

@JoshuaSelimi 11 лет назад

Can't thank you enough. I've been struggling with this for a while now, but all I had to do was watch this video once - it's all clear now!

@EE-Spectrum 7 лет назад

This is by far the best explanation of first principles l have seen. I have seen other videos, but none has been so simplified. The others rush through the video and explanation without one being able to follow and understand.

@mrpistachos79 3 года назад

This is literally the best maths lesson I have ever received

@esdeuu7661 12 лет назад

Thanks very much, you have guided me through AS Level Maths this year, you clearly explain the concepts clearly and brilliantly and are providing a great service to students. You are a fantastic teacher and human being!

@isabellehaque-bousquet6910 3 года назад

This blew my tiny mind, thank you for explaining it so wonderfully!

@BeautifulRose16 11 лет назад

I UNDERSTAND!!! :D When you understand a concept in maths, you learn to appreciate it, and you're right, it is really clever. THANK YOU!!!

@gna3706 6 лет назад

Bro . i finally get this . God bless u

@Mrwrong3707 12 лет назад

this is the best n most straight forward explaination, thank you very much

@smokeystoveruk 10 лет назад

Who needs to plan lessons when I have you - yet another excellent video!

@EnvisageKenya 5 лет назад

I am a Calculus tourist, and this destination is quite satisfying - I'll hang around for a while

@archjanasivasuthan6252 4 года назад

Definitely a beautiful sight

@waterwaveworks 9 лет назад

This helped a lot, thank you !

@jennyazah2190 4 года назад

Fantastic ...this is now stuck in my head ..thank you sooo much

@georgencube3476 10 лет назад

Brilliant !!! finally got it , thanks

@ExamSolutions_Maths 10 лет назад

Cool

@iiV1P4z 12 лет назад

Ive been watching these for like 4 hours! i have a maths and psychology mock tomorrow and i was meant to revise psychology tonight, but these are just too helpful. Thanks alot man, i guess ill have to try to remember the psychology notes i revised a week ago :L

@MyTreky 11 лет назад

I Have just looked at your tutorial for expansion of brackets I understand it now completely thanks a lot for your videos they really help

@nonotje12 7 лет назад

100% certified no better explanation can be found, trust me.

@iamsopoor9 13 лет назад

Too bad i wont be needing these videos anymore, cheers for the help mate

@jo77771 11 лет назад

This video actually made differentiation interesting! :O

@BrainzIRL 11 лет назад

Eureka !! Thank you so much for this vid, very well put

@soccerhighlightshd9051 6 лет назад

Perfection !!!!

@ExamSolutions_Maths 10 лет назад

thank you

@Ps-pn9qg Год назад

Thanks you explained it so well

@dalaxdercrisper957 8 лет назад

Thanks for teaching me so simple even Math is my weakest subject but that doesn't stop me from learning. I managed to learn a little.

@ExamSolutions_Maths 8 лет назад

+saifuddin jamil Keep at it and it does get easier. Good luck.

@dalaxdercrisper957 8 лет назад

ExamSolutions Thanks.

@ExamSolutions_Maths 13 лет назад

@joooooooytalks No probs - pleased to have your support

@Buttontheplay 10 лет назад

Thank you so much

@ExamSolutions_Maths 11 лет назад

Well done

@dmmath-tutor5769 8 лет назад

Brilliant!

@raimsa4081 9 лет назад

you a genious

@oshina8433 9 лет назад

thanks a lot

@the81kid 5 лет назад

Thanks a lot! A very clear and good explanation!

@ExamSolutions_Maths 5 лет назад

Thank you. I am pleased it helped.

@ExamSolutions_Maths 13 лет назад

@mark94uk Excellent - congratulations

@satadhi 10 лет назад

fantastic

@ExamSolutions_Maths 11 лет назад

You could think of it as difference. difference in y over difference in x

@ExamSolutions_Maths 12 лет назад

I would need to see all your working

@ExamSolutions_Maths 11 лет назад

You're welcome

@ExamSolutions_Maths 12 лет назад

Pleasure.

@stevedl3150 11 лет назад

I`ve looked over your brilliant website. Have you any plans to make some videos on Geometry ? I mean simple Geometry, such as proofs of Geometric shapes, and proof of congruity between Geometric shapes, and proof that angle "x" equals angle "y" etc.

@maha_13 4 года назад

amazing

@rockgeo3816 8 лет назад

Thanks for the explanation once again ;D.

@ExamSolutions_Maths 8 лет назад

+Rock Geo That's okay

@RAINx-op7zl 3 года назад

You have no idea how much you helped me 🥳

@ExamSolutions_Maths 3 года назад

Best wishes and I hope you will be able to now make progress on this.

@Godz18saints 10 лет назад

Brilliant

@archjanasivasuthan6252 4 года назад

Beautiful

@Clouds095 11 лет назад

Ahh I need to watch it from the start ; as soon as i saw this it looked like the definition of a limit (of a function)

@salatansimbajon3455 2 месяца назад

Yes, i got it

@ExamSolutions_Maths 13 лет назад

@iamsopoor9 Thanks for your donation. All the best to you.

@iiV1P4z 12 лет назад

@ExamSolutions ill have an hour break in between the exams and ive managed to cram an hour in tonight, so hopefully ill be alright. and thanks anyway :) if i manage to pull it through in maths (thanks to this) ill probably donate some :)

@dheevesh16 6 лет назад

If you don't find this beautiful, you have no heart.

@RuhabDabeer 5 лет назад

I find this guy really great at teaching You must live in America If you have teachers like that

@shahtayyib 4 года назад

@@RuhabDabeer he's literally British 😭

@RuhabDabeer 4 года назад

@@shahtayyib ik man What I meant is You find teachers like him at America

@dedly13 12 лет назад

thankyou

@debbiehariette6335 7 лет назад

you are a good teacher!! thank you for this!

@ontheway5792 6 лет назад

Could u tell me what's the meaning of "H tend to 0" ?

@243liverpool 4 года назад

@@ontheway5792 gets closer and closer to 0 but never gets to 0

@ontheway5792 4 года назад

@@243liverpool ahahahahhahahahahahhahahha that was 2 years from now!! LOOOOL!! Anyway, thank you 😁😁😄😄

@243liverpool 4 года назад

ٍScience is the best! 😂😂well I hope you did well in your a levels or whatever it was u needed this info for 😂

@ontheway5792 4 года назад

@@243liverpool Yeah, man I got A in A level Maths thanks to that great man, Sir Stuart....😍😍😍

@ExamSolutions_Maths 12 лет назад

@iiV1P4z Good luck with the psychology, it looks like you are goping to need it.

@xXCosmicstrikeXx 10 лет назад

Its not just for the y=x^2 graphs. y=4x^5 does have a gradient function of dy/dx=20x^4 :)

@GEMINDIGO 3 года назад

An excellent video which explains the concepts clearly and concisely but why didn't you go all the way to the general limit function f(x+h)-f(x)/x+h-x?That would have really finished the explanation!

@guoxiong96 10 лет назад

EXCELLENT!! I FINALLY UNDERSTAND ABOUT DIFFRENTIATION. Anyway I had a question here. Is dy/dx is only for y=x^2 graph? and what if my question is y=4x^5, after dy/dx will be y=20x^4. but y=x^5 is not a y=x^2 graph. Can you help me out on this? Thank you!

@naturaldon 12 лет назад

@smokeeeeeeeee Yeah of course. I will change my ucas/saq shortly.

@igormazur9662 8 лет назад

Very useful videos but he speaks a bit like Bear Grylls

@kagamitma Год назад

good

@rishabhvegeta 11 лет назад

@lickmyshoe182 the answer to this question is 2x. its easy all u have to do is write d/dx(x^2+2) and differentiate each separately. x^2 differentiation will be 2x and that of 2 will be 0 as it is a constant value. the formula of differentiation is nx^n-1..:)

@certifiedYGshai 9 лет назад

Hi, i tried to differentiate the line of x^3 but, although i did when i used the formula, i didn't get 3x^3 when i used the 'first principle' method: i got x^3+3x^2+3xh+h^2, do you have any idea of what i may have done wrong?

@TheHDSuperLow 10 лет назад

Do they ask questions on this in the exam?

@alasdairking6241 2 года назад

10 years late to the party but this is a brilliant video thank you very much!!!

@ExamSolutions_Maths 2 года назад

Never late buddy. We're still making videos !

@JoeyohNoey 10 лет назад

Why did you say "you'll end up with 3x squared," while point at the 2x?

@MyTreky 11 лет назад

Expansion done could you explain it plz.thanks

@rm9994 4 года назад

So we are trying to get closer and closer to the tangent gradient. So why not just take points on the tangent line to measure gradient?

@alakazam7896 11 лет назад

what would d/dx mean? or d^2y/dx^2 mean tho?

@mara-tr9ix 3 года назад

you absolute g

@SalamProductions 11 лет назад

Basically: Gradient of Cord is Dif in y / Dif in x, which is the closest estimate for the Gradient of the Tangent. Therefore: Dif in y / Dif in x = dy/dx. See that pattern? Gradient of Cord = dif y/ dif x Gradient of Tangent = dy/dx

@alakazam7896 11 лет назад

just started C3 and ive always wanted to know how differentiation was made because my teacher just gave me the equation and i just had to accept it, one question, what does the d stand for in dy/dx?

@ExamSolutions_Maths 11 лет назад

Not at the moment, sorry. More A-level stuff is to be done this academic year.

@Clouds095 11 лет назад

Why is the derivative of x^n nax^n-1 ; do you have a proof video for this ?

@CZ17J 11 лет назад

i dont understand i got that but i thought if h tends to 0 then both 3xh and h^2 would = zero so altogether it = 3x^2 which is that you get from dy/dx. is that not right?

@hydrox24 10 лет назад

Great videos, what software do you use to do the drawing and note-creation? It looks quite useful.

@WanSyazlina 9 лет назад

Thank you! thank you! thank you! Your explanation was clear and easy to understand. :)

@ExamSolutions_Maths 9 лет назад

Wan Syazlina Wan Asim Thank you for viewing it.

@samhughes711 5 лет назад

Thank you so much you've saved me hours of headache!

@ExamSolutions_Maths 5 лет назад

No problem, pleased to hear it helped.

@samisiddiqi5411 3 года назад

8:40

@PaperPlanes021 12 лет назад

For y=x^3 I keep getting 3x^2 + 3xh + h^2 ...any ideas as to what I'm doing wrong?

@JoyErnst 12 лет назад

Remember that h tends to zero, so 3xh and h^2 cancel.

@guoxiong96 10 лет назад

and another question is y=x^3, after dy/dx should be y=3x^2, but if you are calculating the 2 points points (x, x^3) and [(x+h), (x+h)^3], in the end I got the gradient was 3x + h^2. If you are doing h=0, therefore it's only y=3x. It doesn't match the answer of dy/dx which is y=3x^2. Kindly let me know about the questions thanks maybe I did not understand well.

@lukedepledge2812 8 лет назад

👍👍🏿

@guoxiong96 10 лет назад

but you can try using the same method of calculating the 2 points, in the end the answer isn't 20x^4. Unless you directly dy/dx it refer to my replies below (2 days ago) about the y=x^3

@bobbuilder22 5 лет назад

I LOVE YOU

@bobbuilder22 5 лет назад

YOU ARE MY LIFESAVER MARRY ME

@bobbuilder22 5 лет назад

I WOULD ACTUALLY FAIL MATHS AND BE NOTHING WITHOUT YOU

@alexmiller5347 8 лет назад

I understand till 7:22 what happened to the 2 and - 2 in the denominator. Where did they go?

@alexmiller5347 8 лет назад

Loooool they cancel out

@naturaldon 12 лет назад

@smokeeeeeeeee 100% in c1,c2,c3,m1,m2,s1,d1,fp1 and 97% in s2 :( Plus you are looking at the UMS scores not the actual mark out of 75. I applied for maths at cambridge, still can't believe it? :)

@lickmyshoe182 11 лет назад

what about for y=x^2+2? I'm confused :S

@harzzzyh845 9 лет назад

In the C1 exam would you be asked to prove this ?

@ExamSolutions_Maths 9 лет назад

Harsimran Sekhon Unlikely but you should be aware of the concept.

@harzzzyh845 9 лет назад

Okay thanks

@jamestaylor6757 10 лет назад

I don't understand how you get 4+4h+h^2 - 4 from (2+h)^2 - 4 I'm assuming I'm missing some basic maths..? Please help!

@ExamSolutions_Maths 10 лет назад

(2+h)(2+h)=4+2h+2h+h^2 when expanded This simplifies to 4+4h+h^2 Then put on the last term -4

@jamestaylor6757 10 лет назад

Ah, I should have expanded out first! Many thanks!!!

@BrownKow100 12 лет назад

h approaches 0, so you would end up with 3x^2

@kGCryTeK 9 лет назад

At 10:21 I don't understand why the denominator doesn't stay as x+h-x. Why does it change to just h?

@AhmedKhan-dj4ti 8 лет назад

+Reece Cameron x cancels out ..

@SarangKdancecovers 8 лет назад

+Reece Cameron x - x = cancels :-)

@khromburst6671 7 лет назад

Came up in 2016 c1 OCR

@anotherdoseyt 7 лет назад

kHromBurst what

@AsadulIslam24434 9 лет назад

4:32, why do you have to square the 2.0001? I don't quite understand.

@ExamSolutions_Maths 9 лет назад

Because the curve is y=x^2, you square the x. That has been done in all the previous diagrams.

@AsadulIslam24434 9 лет назад

ExamSolutions ok. Thank you very much.

@naturaldon 13 лет назад

my maths results: maths 100% further maths 99% :D :D :D

@gaminghats813 4 года назад

congrats even though im 8 years too late

@rm9994 5 лет назад

What if it isn’t y= x^2 what if it is a random line going in different directions. Also what is the proof. Ok multiplying by the power then reducing it works in most cases. But this isn’t an explanation or proof. Why not reduce the power by 2. What is the understanding behind this power multiplication then reduction. It is explained no where.