Differentiation from 1st Principles | Calculus by ExamSolutions

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  • Опубліковано 25 гру 2024

КОМЕНТАРІ • 154

  • @faruzsyed
    @faruzsyed 7 років тому +1

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

  • @hoi288
    @hoi288 10 років тому +46

    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
      @ExamSolutions_Maths  10 років тому +5

      You're welcome

    • @raimsa4081
      @raimsa4081 9 років тому +2

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

    • @ioft8542
      @ioft8542 2 роки тому

      you're welcome

  • @robertbrodie9566
    @robertbrodie9566 5 років тому +25

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

  • @Almilany95
    @Almilany95 12 років тому +2

    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

  • @pleasework96
    @pleasework96 11 років тому +110

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  12 років тому +3

    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
    @sleepyyymoon 9 років тому +26

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

  • @callummatchett8937
    @callummatchett8937 10 років тому +19

    I like how he writes the letter ' f '

  • @EE-Spectrum
    @EE-Spectrum 7 років тому

    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.

  • @JoshuaSelimi
    @JoshuaSelimi 11 років тому +1

    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!

  • @mrpistachos79
    @mrpistachos79 4 роки тому +2

    This is literally the best maths lesson I have ever received

  • @EnvisageKenya
    @EnvisageKenya 5 років тому +1

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

  • @georgencube3476
    @georgencube3476 11 років тому +15

    Brilliant !!! finally got it , thanks

  • @nonotje12
    @nonotje12 7 років тому

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

  • @esdeuu7661
    @esdeuu7661 12 років тому

    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!

  • @dalaxdercrisper957
    @dalaxdercrisper957 8 років тому +3

    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.

  • @BeautifulRose16
    @BeautifulRose16 12 років тому

    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!!!

  • @iiV1P4z
    @iiV1P4z 13 років тому +1

    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

  • @isabellehaque-bousquet6910
    @isabellehaque-bousquet6910 3 роки тому

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

  • @gna3706
    @gna3706 7 років тому +1

    Bro . i finally get this . God bless u

  • @iamsopoor9
    @iamsopoor9 13 років тому

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

  • @MyTreky
    @MyTreky 11 років тому

    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

  • @Ps-pn9qg
    @Ps-pn9qg 2 роки тому +1

    Thanks you explained it so well

  • @Mrwrong3707
    @Mrwrong3707 12 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  11 років тому +2

    thank you

  • @smokeystoveruk
    @smokeystoveruk 11 років тому

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

  • @jennyazah2190
    @jennyazah2190 4 роки тому

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

  • @jo77771
    @jo77771 11 років тому +1

    This video actually made differentiation interesting! :O

  • @debbiehariette6335
    @debbiehariette6335 8 років тому +1

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

    • @ontheway5792
      @ontheway5792 7 років тому +1

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

    • @243liverpool
      @243liverpool 5 років тому

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

    • @ontheway5792
      @ontheway5792 5 років тому

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

    • @243liverpool
      @243liverpool 5 років тому

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

    • @ontheway5792
      @ontheway5792 5 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  13 років тому

    @joooooooytalks No probs - pleased to have your support

  • @RAINx-op7zl
    @RAINx-op7zl 4 роки тому

    You have no idea how much you helped me 🥳

    • @ExamSolutions_Maths
      @ExamSolutions_Maths  4 роки тому

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

  • @soccerhighlightshd9051
    @soccerhighlightshd9051 7 років тому +2

    Perfection !!!!

  • @waterwaveworks
    @waterwaveworks 9 років тому +1

    This helped a lot, thank you !

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  11 років тому +1

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

  • @dheevesh16
    @dheevesh16 6 років тому +17

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

    • @RuhabDabeer
      @RuhabDabeer 5 років тому

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

    • @shahtayyib
      @shahtayyib 4 роки тому +1

      @@RuhabDabeer he's literally British 😭

    • @RuhabDabeer
      @RuhabDabeer 4 роки тому +3

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

  • @raimsa4081
    @raimsa4081 9 років тому +3

    you a genious

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  11 років тому

    Well done

  • @BrainzIRL
    @BrainzIRL 12 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  11 років тому

    You're welcome

  • @iiV1P4z
    @iiV1P4z 13 років тому

    @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 :)

  • @the81kid
    @the81kid 6 років тому

    Thanks a lot! A very clear and good explanation!

  • @stevedl3150
    @stevedl3150 11 років тому

    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.

  • @alasdairking6241
    @alasdairking6241 2 роки тому

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

  • @guoxiong96
    @guoxiong96 11 років тому +1

    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!

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  13 років тому

    @mark94uk Excellent - congratulations

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  12 років тому

    Pleasure.

  • @GEMINDIGO
    @GEMINDIGO 4 роки тому

    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!

  • @rockgeo3816
    @rockgeo3816 9 років тому +1

    Thanks for the explanation once again ;D.

  • @oshina8433
    @oshina8433 10 років тому +1

    thanks a lot

  • @TheHDSuperLow
    @TheHDSuperLow 10 років тому +1

    Do they ask questions on this in the exam?

  • @dmmath-tutor5769
    @dmmath-tutor5769 8 років тому

    Brilliant!

  • @xXCosmicstrikeXx
    @xXCosmicstrikeXx 11 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  12 років тому

    I would need to see all your working

  • @rishabhvegeta
    @rishabhvegeta 12 років тому

    @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..:)

  • @alexmiller5347
    @alexmiller5347 8 років тому

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

  • @SalamProductions
    @SalamProductions 11 років тому

    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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  13 років тому

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

  • @satadhi
    @satadhi 11 років тому +1

    fantastic

  • @kGCryTeK
    @kGCryTeK 9 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  13 років тому

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

  • @AsadulIslam24434
    @AsadulIslam24434 10 років тому

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

    • @ExamSolutions_Maths
      @ExamSolutions_Maths  10 років тому

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

    • @AsadulIslam24434
      @AsadulIslam24434 10 років тому

      ExamSolutions ok. Thank you very much.

  • @archjanasivasuthan6252
    @archjanasivasuthan6252 4 роки тому +1

    Beautiful

  • @JoeyohNoey
    @JoeyohNoey 10 років тому +2

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

  • @Clouds095
    @Clouds095 11 років тому

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

  • @alakazam7896
    @alakazam7896 11 років тому +1

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

  • @Clouds095
    @Clouds095 11 років тому

    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)

  • @WanSyazlina
    @WanSyazlina 9 років тому

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

  • @Buttontheplay
    @Buttontheplay 10 років тому

    Thank you so much

  • @certifiedYGshai
    @certifiedYGshai 9 років тому

    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?

  • @rm9994
    @rm9994 5 років тому

    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?

  • @jamestaylor6757
    @jamestaylor6757 11 років тому +1

    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
      @ExamSolutions_Maths  11 років тому +1

      (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
      @jamestaylor6757 11 років тому

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

  • @ExamSolutions_Maths
    @ExamSolutions_Maths  11 років тому

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

  • @salatansimbajon3455
    @salatansimbajon3455 7 місяців тому

    Yes, i got it

  • @CZ17J
    @CZ17J 11 років тому

    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?

  • @Godz18saints
    @Godz18saints 10 років тому

    Brilliant

  • @harzzzyh845
    @harzzzyh845 9 років тому +2

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

  • @hydrox24
    @hydrox24 11 років тому

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

  • @alakazam7896
    @alakazam7896 11 років тому

    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?

  • @dedly13
    @dedly13 13 років тому

    thankyou

  • @samhughes711
    @samhughes711 5 років тому

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

  • @kagamitma
    @kagamitma 2 роки тому +1

    good

  • @igormazur9662
    @igormazur9662 8 років тому +5

    Very useful videos but he speaks a bit like Bear Grylls

  • @MyTreky
    @MyTreky 11 років тому

    Expansion done could you explain it plz.thanks

  • @naturaldon
    @naturaldon 13 років тому

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

  • @guoxiong96
    @guoxiong96 11 років тому

    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

  • @PaperPlanes021
    @PaperPlanes021 12 років тому

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

  • @bobbuilder22
    @bobbuilder22 6 років тому +1

    I LOVE YOU

    • @bobbuilder22
      @bobbuilder22 6 років тому +1

      YOU ARE MY LIFESAVER MARRY ME

    • @bobbuilder22
      @bobbuilder22 6 років тому +1

      I WOULD ACTUALLY FAIL MATHS AND BE NOTHING WITHOUT YOU

  • @mara-tr9ix
    @mara-tr9ix 4 роки тому

    you absolute g

  • @guoxiong96
    @guoxiong96 11 років тому

    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.

  • @JoyErnst
    @JoyErnst 12 років тому

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

  • @samisiddiqi5411
    @samisiddiqi5411 3 роки тому

    8:40

  • @naturaldon
    @naturaldon 13 років тому +1

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

    • @gaminghats813
      @gaminghats813 5 років тому +2

      congrats even though im 8 years too late

  • @naturaldon
    @naturaldon 13 років тому

    @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? :)

  • @rm9994
    @rm9994 6 років тому +1

    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.

  • @leonleon1993
    @leonleon1993 13 років тому

    First :D !!!!!!!!!!!

  • @knap-dalf2215
    @knap-dalf2215 9 років тому

    How can h ever be zero when we are dividing by h earlier on???

    • @ExamSolutions_Maths
      @ExamSolutions_Maths  9 років тому +1

      Knap- dalf h is not zero, it tends to zero. 0.00000000000............01

    • @knap-dalf2215
      @knap-dalf2215 9 років тому +1

      How do we "get rid of" zero at all then? Thanks for replying :-)

    • @ExamSolutions_Maths
      @ExamSolutions_Maths  9 років тому +1

      Knap- dalf h is so small, infinitesimal that we can ignore it

    • @knap-dalf2215
      @knap-dalf2215 9 років тому +3

      ExamSolutions Okay, I see now :-)

  • @BrownKow100
    @BrownKow100 12 років тому

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

  • @lukedepledge2812
    @lukedepledge2812 8 років тому

    👍👍🏿

  • @michaeldoyle2550
    @michaeldoyle2550 3 роки тому

    This is a great explanation but god this subject is mind numbing

  • @khromburst6671
    @khromburst6671 7 років тому

    Came up in 2016 c1 OCR