Differentiation from 1st Principles | Calculus by ExamSolutions
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- Опубліковано 17 сер 2011
- 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).
For more videos on differentiation look at the playlist
DIFFERENTIATION (1) PLAYLIST at • Differentiation (1)
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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!
You're welcome
***** lol maybe we have the same lecture "draw a grah and just point at it" hahaha
you're welcome
i dont think anyone has ever explained the first principle better than this gentleman . Its compact enough and yet comprehensive. Many thanks!!
This is the simplest explanation on the whole of youtube... trust me i know
just done the same tour totally agreed
haha!
Nice comment. Happy new year for 2021
You just taught me in 14 mins what my maths teacher couldn't in 1 hour
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.
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
I like how he writes the letter ' f '
This is very clear, thank you, your videos are lifesavers :)
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!
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.
This is literally the best maths lesson I have ever received
I am a Calculus tourist, and this destination is quite satisfying - I'll hang around for a while
Definitely a beautiful sight
Brilliant !!! finally got it , thanks
Cool
This blew my tiny mind, thank you for explaining it so wonderfully!
Too bad i wont be needing these videos anymore, cheers for the help mate
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!
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!!!
Bro . i finally get this . God bless u
100% certified no better explanation can be found, trust me.
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.
+saifuddin jamil Keep at it and it does get easier. Good luck.
ExamSolutions
Thanks.
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
This helped a lot, thank you !
Who needs to plan lessons when I have you - yet another excellent video!
this is the best n most straight forward explaination, thank you very much
thank you
Perfection !!!!
This video actually made differentiation interesting! :O
Fantastic ...this is now stuck in my head ..thank you sooo much
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
Eureka !! Thank you so much for this vid, very well put
Thanks you explained it so well
You could think of it as difference. difference in y over difference in x
you a genious
thanks a lot
@joooooooytalks No probs - pleased to have your support
Thank you so much
Well done
Brilliant!
Thanks a lot! A very clear and good explanation!
Thank you. I am pleased it helped.
fantastic
Thanks for the explanation once again ;D.
+Rock Geo That's okay
You have no idea how much you helped me 🥳
Best wishes and I hope you will be able to now make progress on this.
I would need to see all your working
@mark94uk Excellent - congratulations
10 years late to the party but this is a brilliant video thank you very much!!!
Never late buddy. We're still making videos !
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.
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)
amazing
You're welcome
@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 :)
Beautiful
you are a good teacher!! thank you for this!
Could u tell me what's the meaning of "H tend to 0" ?
@@ontheway5792 gets closer and closer to 0 but never gets to 0
@@243liverpool ahahahahhahahahahahhahahha that was 2 years from now!! LOOOOL!! Anyway, thank you 😁😁😄😄
ٍScience is the best! 😂😂well I hope you did well in your a levels or whatever it was u needed this info for 😂
@@243liverpool Yeah, man I got A in A level Maths thanks to that great man, Sir Stuart....😍😍😍
Brilliant
@iiV1P4z Good luck with the psychology, it looks like you are goping to need it.
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!
Its not just for the y=x^2 graphs. y=4x^5 does have a gradient function of dy/dx=20x^4 :)
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!
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?
Pleasure.
Do they ask questions on this in the exam?
@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..:)
Why did you say "you'll end up with 3x squared," while point at the 2x?
Yes, i got it
@iamsopoor9 Thanks for your donation. All the best to you.
Very useful videos but he speaks a bit like Bear Grylls
thankyou
what would d/dx mean? or d^2y/dx^2 mean tho?
Not at the moment, sorry. More A-level stuff is to be done this academic year.
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?
If you don't find this beautiful, you have no heart.
I find this guy really great at teaching
You must live in America If you have teachers like that
@@RuhabDabeer he's literally British 😭
@@shahtayyib ik man
What I meant is
You find teachers like him at America
good
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
@smokeeeeeeeee Yeah of course. I will change my ucas/saq shortly.
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?
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?
Why is the derivative of x^n nax^n-1 ; do you have a proof video for this ?
Expansion done could you explain it plz.thanks
you absolute g
For y=x^3 I keep getting 3x^2 + 3xh + h^2 ...any ideas as to what I'm doing wrong?
Remember that h tends to zero, so 3xh and h^2 cancel.
Great videos, what software do you use to do the drawing and note-creation? It looks quite useful.
8:40
In the C1 exam would you be asked to prove this ?
Harsimran Sekhon Unlikely but you should be aware of the concept.
Okay thanks
Thank you so much you've saved me hours of headache!
No problem, pleased to hear it helped.
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.
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
I understand till 7:22 what happened to the 2 and - 2 in the denominator. Where did they go?
Loooool they cancel out
@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? :)
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!
(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
Ah, I should have expanded out first!
Many thanks!!!
Thank you! thank you! thank you! Your explanation was clear and easy to understand. :)
Wan Syazlina Wan Asim Thank you for viewing it.
At 10:21 I don't understand why the denominator doesn't stay as x+h-x. Why does it change to just h?
+Reece Cameron x cancels out ..
+Reece Cameron x - x = cancels :-)
what about for y=x^2+2? I'm confused :S
h approaches 0, so you would end up with 3x^2
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YOU ARE MY LIFESAVER MARRY ME
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4:32, why do you have to square the 2.0001? I don't quite understand.
Because the curve is y=x^2, you square the x. That has been done in all the previous diagrams.
ExamSolutions ok. Thank you very much.
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.
This is a great explanation but god this subject is mind numbing
👍👍🏿
Came up in 2016 c1 OCR
kHromBurst what
expanding (x+h)^3 wrong i should think