Differentiation, Explained 📈 [A-Level Maths, Year 1 & 2]

[@M10-y3b]

36:27 Should be multiplied by 2^(x^2) instead of 2^x? Thanks for the video btw

[@BicenMaths]

Correct! I’m gonna pin this comment. Well done for noticing the error!

[@cysage5876]

Why is this the case?

[@urboy_raz]

I was going mad until I saw this comment, Tnx bruv

[@KayKay-rg5ds]

dude I'm crying this guy is the best you deserve all the love in the world bro ily

[@nadernassr6636]

This style is so intruging. Gets me more engaged honestly.

[@chris5207]

this video needs to be used by exam boards as a revision resource - really well put together - thank you !

[@BicenMaths]

What a lovely compliment - thanks!

[@shellybelly1071]

Thank you so much! Commenting so that the algorithm boosts this gem!

[@henryash413]

22:45 missing cut 23:12 missing cut 29:06 missing cut no hate, great vid, just fyi

[@WilliamCooper2005]

This was very helpful and well explained. You and TL maths make A level maths so much easier!

[@BicenMaths]

Thank you!

[@orangecamo_cinnamonrolls306]

Thank you, these videos are the BEST. They definitely help with my understanding of maths. I'm aware that lots of people have asked for certain topics so you've probably already got a lot to do, but it'd be amazing if you could do a video on modelling! Thanks again :)

[@BicenMaths]

Thanks for this lovely comment! I’ll add modelling to my list of ideas 👍🏼

[@harryhazard719]

Thanks a lot, the same for integration would be very useful and all of the other main topics like sequences and series or coordinate geometry 👍

[@BicenMaths]

Love these suggestions! In the mean time you find these I have made on integration useful: Theory: kzbin.info/www/bejne/gme4nJ2febugjc0 Examples: kzbin.info/www/bejne/pmSWiaJ9jJySjJo

[@ToriKo_]

@@BicenMaths Have those been made yet? I found this very useful, tho I was a bit lost searching through your integration playlist

[@BicenMaths]

No I haven’t made them yet - been too busy with exams! 😱

[@Sophie-uc1et]

I’m currently on a B but need an A* , I’m working really hard , thank you for your videos , I hope I get into my dream uni 😭

[@BicenMaths]

I wish you all the best, and hope you get into your dream uni too! 🤞🏼

[@ren952]

the best video ive ever watched on differentiation. have aqa paper 1 tommorowlitteraly life saving

[@saloon241]

I am two minutes in and this is already so helpful. Somehow the basic notations were just never taught in my classes (also took a few years off maths so I've forgotten some as well) and despite being in uni they still haven't clicked. I'm trying to fill in any gaps I can for going into next year because learning without really solid basics is almost impossible.

[@BicenMaths]

Good luck with your studies! Thanks for the lovely comment 👍🏼

[@xubarney1326]

This is so clear! You are a life saver. So cool!

[@ryou6453]

you sir have saved my a level maths I rly appreciate it

[@BicenMaths]

You're welcome! Let me know if there's anything else I can do to help!

[@ABDULLAMAHMOOD-s6n]

great video. gives you better understanding about the subject than most teachers do. keep it up

[@BicenMaths]

Thank you!

[@khalisa6904]

This has really helped me for my exam tomorrow in maths, thank you

[@BicenMaths]

You’re welcome! Pleased the video has helped you 👍🏼

[@stillfl3]

This was so helpful, the layout is great and you walk through it very nicely

[@saqeenasultananoor8297]

I did not have pure maths in my IGCSEs, but I do now in my Alevels, I always had difficulty with the concepts of differentiation, thank you so much for this video, I have my upcoming P34 exam this week! helped me a lot!

[@BicenMaths]

Thanks for sharing - good luck with your exams!

[@lillyidk1358]

Thank you so much you’re the best you make maths understandable!!😭❤️

[@BicenMaths]

Thank you!

[@siennathompson2969]

What condition needs to be met to use the chain rule originally, e^x --> e^x but when we use the chain rule, e^x --> e^x * x'

[@BicenMaths]

Well this technically is still the chain rule, as the derivative of x (x’) is just 1, so you are multiplying by 1. The chain rule’s conditions are that the function you are differentiating is a composite function. If you check out my full differentiation playlist you’ll see this part explained in more detail!

[@birgitfischer8031]

Hi, I've gotten a little muddled up on the optimisation 25:07 . When you take the sqrt of 2000, wouldn't you get plus or minus 44.7? And then if t = 44.7 -> C = 20.94; if t = -44.7 -> C = 3.06. So -44.7 minimises C. However, taking the second derivative with t = -44.7 will be greater than 0 suggesting that it is a maximum, and as you did taking the second derivative with t = 44.7 is less than 0 so it is a minimum yet the answer it produces is greater. I am not sure why this is or have I made a mistake? Thank you in advance!

[@BicenMaths]

The wording of my question isn’t perfect - it should probably say that t>0, otherwise you could set t as -0.001 (for example) and get a negative cost, which doesn’t make any sense! So please imagine that the question says that the temperature must be >0. Otherwise all your calculations are correct!

[@birgitfischer8031]

@@BicenMaths Thank you very much! I assumed that may be the case. That makes sense.

[@ikunim_]

Thanks so much for the video sir!

[@BicenMaths]

My pleasure!

[@sidec7673]

Thank you for everything sir

[@nambulakm]

invaluable video, thank you so much!

[@zektric5684]

Hey Sir, you might recognise my username / profile picture, I commented a lot on this channel aha, I recently sat my year 13 A Level Mock exams and went from a very bad grades in my year 12 exams (I revised a lot but it didnt click until a few months ago) to A* in both pure papers and A in my mechanics paper, thanks to my hard work and your amazing teaching! Thank you so much.

[@BicenMaths]

Of course I remember “Zektric”, you commented so much and asked some great questions! This is amazing news, I’m so pleased you’ve achieved such incredibly high grades in your mock. Well done for all your hard work, and thank you for saying that my teaching played a part in it (it was all down to you and your dedication). Keep up the hard work, well done! 👏🏼

[@zektric5684]

@@BicenMaths Thank you!

[@zai9184]

congrats

[@clowd1e449]

Hey, just wanted to ask how many hours did u revise?

[@mt1778]

This was extremely helpful. Can you please make a vid on Integration (both years)? A vid on Mechanics and Statistics (both years) would be extremely helpful too. Considering the exams are only a month away, pls post these topics asap Thanks

[@BicenMaths]

I'm planning to do integration soon, but here's something that you'll find helpful on it from before: kzbin.info/www/bejne/gme4nJ2febugjc0 and kzbin.info/www/bejne/pmSWiaJ9jJySjJo ... and something for Stats: kzbin.info/www/bejne/jajZh6iGbpuLoMU ... and lastly, something for Mechanics: kzbin.info/www/bejne/ioiQmoChe5qcgNk Good luck!

[@mt1778]

@@BicenMaths Thanks. Do you know when that will be posted approximately?

[@BicenMaths]

@@mt1778 Unfortunately not in time for your exams, have got too much I'm doing to support my exam students in school right now! But the 2 integration videos I've sent you will be great for revision.

[@Panbxb]

36:53 How is it not 18 ? 1)since 2sin3§ will diff to 6cos3§ 2)then using chain rule we multiply 6cos3§ by the derivative of 3§ which is 3 3) 6cos3§ x 3 = 18cos3§

[@BicenMaths]

When you do 1) in your answer, you have already used the chain rule - so you don't need to use it again. When you first learn how to differentiate sin(kx) for example, and you are told it is kcos(kx), this is just an application of the chain rule.

[@aminakhatunmim2911]

This is the best video of differentiation😭😭😭😭😭😭 can you please solve some papers of CIE too? 😭😭😭

[@audify3833]

could some of these be done for further maths or is it an inconvenience since not many people take it?

[@BicenMaths]

It isn’t an inconvenience! I’m just prioritising maths content right now. If you check my homepage there are videos for every chapter of core pure for further maths, plus further mechanics 👍🏼

[@john1372]

Great video and I’m sure some people are hoping to see your “Integration, Explained”

[@BicenMaths]

I know, I have just been so busy! Hoping to get around to it eventually

[@rahandsaid55]

@@BicenMaths pls do it quick we are in exam szn

[@BicenMaths]

Been too busy working at my school 😱

[@Crownmoneyjshd]

at 38:21 it should be be 12tan^2xcotx

[@BicenMaths]

No, tan differentiates to sec^2 not to cot

[@Crownmoneyjshd]

@@BicenMaths my bad sorry

[@eswynplantagenet4483]

41:20- may I ask why it is not 3cos(3x^1/2) and just cos(3x^1/2)? Incredible video btw, as with all your others

[@BicenMaths]

It is just cos(3x^1/2) for the first part of the chain rule, and then the derivative of 3x^1/2 which is 3/2x^-1/2 is added as the next part of the chain rule. The reason there is no 3, is because it is actually more complex and is 3/2x^-1/2 instead. A bit hard to explain, but it's an example of using the chain rule twice!

[@lilsels]

THANK YOU!!! THIS IS AMAZING!!!!!!!!!

[@DanielkaElliott]

What's the subtraction you did at 13:10. How did you get that t^1/6 ???? And what was the y-1 and x-1 when you were finding the tangent and normal from?. Why does DC/Dt have to be 0 for the minimum??

[@BicenMaths]

The subtraction to get 1/6 for the power of t is from 1/2 - 1/3. This is the index law of division. The y-1 and x-1 is from the version of the straight line equation which is y-y1=m(x-x1). dC/dt must equal 0, as things are a maximum or minimum when the gradient is 0.

[@harmey5928]

Hi, sir thank you for all your amazing videos! Would you be able to cover some of the further stats content please? It would be really helpful.

[@BicenMaths]

Maybe in the future! Lots of people have been asking for Further Stats, so I’ll try and get to this soon 👍🏼

[@devashreeroy6391]

these are fantastic

[@BicenMaths]

🙌🏼 thanks!

[@niallquinn6320]

Phenomenal teacher !

[@BicenMaths]

🙌🏼

[@swipez_yt1741]

This is amazing, thank you for the video. Is it possible to make this style of videos for integration and all the other topics in maths?

[@BicenMaths]

Here’s a playlist with all the ones I’ve done so far! Integration is slightly different as it’s just for Year 2, but it does a similar job!

[@swipez_yt1741]

@@BicenMaths I don't see the playlist. Please can I have the link?

[@BicenMaths]

kzbin.info/aero/PL0SSkmc4r_BYSip9_M2qwNYeul20_svb2 I didn’t paste it 🤦🏻‍♂️ Long day!

[@pluto_kun]

This video is amazing thank you so much!!

[@BicenMaths]

Glad it helped!

[@rhett-says-hullo4229]

differentiation and integration are the most difficult sections im tempted to rip those pages out

[@BicenMaths]

😂 Don’t do it! Perseverance will get you there with these topics. Good luck!

[@Was12249]

25:36 can you just leave the root of 2000 and not convert it into a decimal then sub it into C= then round it because wont you lose a mark for rounding or something ?

[@BicenMaths]

Yeah that’s fine - although no marks should be lost in the exam for this, as long as the rounding done isn’t too severe!

[@aida_505]

36:06 how does it become ln2? - oso thank you for this video, i was very blur with this topic and you explained it very well

[@BicenMaths]

This is because a^x functions differentiate to lna multiplied by a^x. So in this case, you get the ln2 as the base is 2. Pleased the video has helped you!

[@aida_505]

@@BicenMaths ohhh i see i see thank youu!

[@hassanshawky123]

Hi Mr. Bicen, thanks for the great videos, can I ask you which App. are you using for hand writing on Ipad ? Thanks again for your help.

[@BicenMaths]

It’s GoodNotes!

[@hassanshawky123]

@@BicenMaths @Bicen Maths oh, thanks, and what about the App you used in the older videos, like the one in this video? 👇 kzbin.info/www/bejne/imbKe6qXrNGKp6s

[@BicenMaths]

This is also GoodNotes, it’s just a recording of the whole screen rather than edited to a smaller size!

[@samuelbrodie1060]

So does the second derivative only give you information about stationary points?

[@BicenMaths]

It tells you about the stationary points, and if they are maximum or minimum points - but it actually tells you about whether the curve is convex or concave at a particular point too. This is covered in Year 2 Differentiation.

[@samuelbrodie1060]

At 24:30, how did you know to make the derivative =0?

[@BicenMaths]

A function is ‘optimised’ (meaning it is a minimum or a maximum) when the gradient is 0, in other words when the derivative is 0.

[@morgan4675]

Where can I find these notes???? Amazing help

[@BicenMaths]

It’s linked in the description, or you can find my Bicen Maths Google Drive in the About section on my channel. Then you can find the folder with Differentiation, Explained. Hope that helps!

[@shamirjilani1496]

Hi, why is it when I differntiate -ln(x+4) by firstly bringing the power forward I get a different answer to when i differentiate -ln(x+4) and dont firstly bring the power forward

[@BicenMaths]

I'm not sure what you mean about bringing the power forward?

[@shamirjilani1496]

@@BicenMaths from -ln(x+4) to ln(x+4)^-1

[@BicenMaths]

Oh I see. -ln(x+4) differentiates to -1/(x+4). If you differentiate ln (x+4)^-1, you get -(x+4)^-2/(x+4)^-1 by the chain rule, which simplifies to -(x+4)^-1 which is the same as -1/(x+4), so they do give the same result!

[@shamirjilani1496]

@@BicenMaths oh ok thank you

[@nathanhawey294]

Thank u bicen.

[@BicenMaths]

My pleasure 👍🏼

[@vai__2609]

thank you so much

[@uvwv]

Great video!!!!!!!

[@H3rx]

Is doing derivatives of sin year 2?

[@BicenMaths]

Yes, it is!

[@primeroxx]

is this for edexcel ial?

[@BicenMaths]

It's for the non-IAL, but it covers the same content!

[@thepythonprogrammer4338]

Hi can you make the same video for intergeration

[@thepythonprogrammer4338]

Love your videos

[@BicenMaths]

Thank you! It’s on my to do list - have just had a very hectic few weeks in my personal life, but hoping to get back to KZbin!

[@kubolor1234]

I'm 27 and still looking for someone to explain differentiation to me.

[@zai9184]

great video

[@EliasCH300]

legend

[@lisaoa4062]

37:47

[@lildj0308x]

Nice