Friday, 30 December 2011

Differentiation

  • Edexcel- C1 Differentiation
  • AQA- C1 Differentiation
  • OCR- C1 Differentiation

One of the new topics, we learn in A-Level Maths is Differentiation. It is one of the branches of Calculus, which is a major field in Mathematics, and almost is a useful application in loads of other fields.. Engineering, Economics, Physics and Chemistry. It is concerned with how one thing changes, as a result of another quantity changes. E.g. How displacement changes, as time changes (dd/ dt) would be the velocity.... We shall look for now at how y changes with respect to x (we call this dy/dx) = d (delta which means change)

We will look at curves, where the gradient is changing at each point on the curve. So dy/dx on each point is different, and not constant. First, i'll introduce you to a tangent. A tangent, is a straight line which touches a point on the curve, it only touches that point though.
The green line is the tangent to the curve( in black), this tangent only touches the yellow point on the curve. Note the gradient at the yellow point, is different to the rest of the points on the curve, because the gradient changes as x changes.

The derivative of a curve is the same as the dy/dx of a function e.g.

The derivative of x^3 = 3x^2
dy/dx (x^3) = 3x^2
This is the first derivative, if differentiate again, we would get the second derivative, again.. the third.. and so on..

dy / dx means differentiating y with respect to x. (what is happening to y, as x changes)

How to Differentiate

To differentiate a function, you reduce the power by 1, and multiply by the new power :

Function          Derivative
axn                 anxn-1

e.g. x^2 
dy/dx = 2x


x^3 
dy/dx = 3x^2


* If we had to differentiate anything to the first power e.g. x , 3x, 5x... it would be 1,3 and 5 respectively. Why ? 
Because it is to the power 1, reducing the power to 0.. anything to the power of 0 equals 1 .. so we just multiply the coefficient of x by 1.. which is the same as taking away the x.

*Differentiating a number .. gives 0. Think about it, if draw a graph of say y = 5, the gradient is 0.

Other Notation 

A function can be written as y =... or f(x) = ..., if we have a function defined as f(x) =...., then the derivative of that is f'(x)=...

f(x) = 5x ... f '(x) = 5 (this is called f prime)

*For the first derivative we use one dash.. second derivative two..etc 
We can only differentiate functions in the form of axn    , so if it looks any different, we have to rearrange to get in that form, using rules of indices.



77 comments:

  1. Great blog! Is your theme custom made or did you download
    it from somewhere? A theme like yours with a few simple adjustements would really make my blog stand out.
    Please let me know where you got your design. Thank you

    Here is my web blog; dolcis waardebon

    ReplyDelete
  2. We have hardware that looks and feels in person -- and compared to the cost and hassle of actual live-blooded pets,
    we sex cams think
    it can be simple. Provided what we want is Windows Phone 7,
    like Windows sex cams Mobile and make the platform seem viable again, or is not, a member of a professional photographer is to.

    I must have access to mobile email, your phone understands German, and" the witch from Delaware" as their candidates.

    ReplyDelete
  3. It's really very difficult in this busy life to listen news on Television, thus I only use internet for that purpose, and obtain the most up-to-date information.

    Take a look at my weblog Mario Lemieux Black Jersey

    ReplyDelete
  4. Excellent write-up. I absolutely appreciate this site.
    Thanks!

    my page; web chat

    ReplyDelete
  5. With havin so much content do you ever run into any
    issues of plagorism or copyright infringement?
    My blog has a lot of completely unique content I've either written myself or outsourced but it seems a lot of it is popping it up all over the internet without my permission. Do you know any solutions to help protect against content from being ripped off? I'd certainly appreciate it.


    my web site ... live cam free sex

    ReplyDelete
  6. Hey, I think your website might be having browser compatibility issues.

    When I look at your blog in Chrome, it looks fine
    but when opening in Internet Explorer, it has some overlapping.
    I just wanted to give you a quick heads up! Other then that,
    fantastic blog!

    Also visit my website :: live chats free

    ReplyDelete
  7. When someone writes an paragraph he/she keeps the
    idea of a user in his/her brain that how a user can know it.

    Therefore that's why this article is outstdanding. Thanks!

    Here is my web site - free chat adult

    ReplyDelete
  8. Hey would you mind sharing which blog platform you're using? I'm planning to start
    my own blog in the near future but I'm having a difficult time selecting between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your design seems different then most blogs and I'm
    looking for something completely unique. P.
    S My apologies for being off-topic but I had to ask!


    Also visit my site; bounceconnect.com

    ReplyDelete
  9. I'm truly enjoying the design and layout of your site. It's a very easy on the
    eyes which makes it much more pleasant for me to come here and visit more often.
    Did you hire out a designer to create your theme?
    Excellent work!

    Here is my web-site ... www.demiurgestudios.com

    ReplyDelete
  10. Can you tell us more about this? I'd want to find out more details.

    Stop by my weblog ... lib.rario.us

    ReplyDelete
  11. Thanks on your marvelous posting! I truly enjoyed reading it, you may be a great author.
    I will be sure to bookmark your blog and will come back someday.
    I want to encourage one to continue your great job, have a nice holiday
    weekend!

    Check out my web blog :: free Live Cam to cam Sex

    ReplyDelete
  12. My coder is trying to convince me to move to .net from PHP.
    I have always disliked the idea because of the expenses.
    But he's tryiong none the less. I've been using WordPress on various websites for
    about a year and am anxious about switching to another platform.
    I have heard fantastic things about blogengine.
    net. Is there a way I can import all my wordpress posts into
    it? Any kind of help would be greatly appreciated!

    my website :: Porn live chat

    ReplyDelete
  13. Hi there, everything is going perfectly here and ofcourse every one is
    sharing data, that's really fine, keep up writing.

    Here is my web-site; lib.rario.us

    ReplyDelete
  14. It's perfect time to make some plans for the long run and it is time to be happy. I've read this publish and if I could I wish to
    suggest you few fascinating issues or advice. Maybe you could write next articles
    relating to this article. I desire to read even more things approximately it!


    Have a look at my weblog :: development.colnotion.com

    ReplyDelete
  15. My spouse and I stumbled over here from a different page and thought I might check things out.
    I like what I see so now i'm following you. Look forward to looking at your web page repeatedly.

    Also visit my website :: free porn cam chat

    ReplyDelete
  16. WOW just what I was searching for. Came here by searching for sexy webcam live

    Here is my weblog - www.skateboard-games.org

    ReplyDelete
  17. Howdy! Do you use Twitter? I'd like to follow you if that would be okay. I'm absolutely enjoying your blog and look forward to new updates.


    Also visit my page; my live web cam

    ReplyDelete
  18. Thank you for the auspicious writeup. It in fact was a amusement account it.
    Look advanced to more added agreeable from you!
    By the way, how could we communicate?

    Look into my website ... porno cam

    ReplyDelete
  19. I love your blog.. very nice colors & theme.
    Did you create this website yourself or did you hire someone
    to do it for you? Plz reply as I'm looking to construct my own blog and would like to find out where u got this from. thank you

    my web page :: sex chats free

    ReplyDelete
  20. Amazing things here. I am very happy to peer your post.
    Thanks a lot and I'm having a look forward to touch you. Will you please drop me a e-mail?

    Review my web blog :: random webcam

    ReplyDelete
  21. Excellent post however I was wanting to know if you could write a litte
    more on this subject? I'd be very grateful if you could elaborate a little bit more. Appreciate it!

    my website ... free web cam sex

    ReplyDelete
  22. Hi, Neat post. There is a problem along with your website in internet
    explorer, might test this? IE nonetheless is the marketplace leader and a large section of other
    people will pass over your wonderful writing due to this problem.


    my web site Nude Live Cam

    ReplyDelete
  23. Hi there! I just wanted to ask if you ever have any trouble with hackers?
    My last blog (wordpress) was hacked and I ended up losing many months of hard work due to no data backup.
    Do you have any solutions to prevent hackers?

    Feel free to visit my web-site: live sex talk

    ReplyDelete
  24. Wow, awesome blog layout! How long have you been blogging for?
    you made blogging look easy. The overall look of your web
    site is fantastic, let alone the content!

    Also visit my weblog; wiki.dbffo.com

    ReplyDelete
  25. I have been browsing online more than 4 hours today,
    yet I never found any interesting article like yours. It is pretty worth enough for me.
    In my view, if all web owners and bloggers made good content as
    you did, the net will be a lot more useful than ever before.


    Review my blog ... http://www.muurahaiset.net/wiki/index.php?title=Good_Advice_On_How_To_Blog_Smarter

    ReplyDelete
  26. Great post. I will be facing many of these issues as well.
    .

    My blog sex chat with cams

    ReplyDelete
  27. Have you ever considered about adding a little bit more than just your articles?
    I mean, what you say is fundamental and all.
    But just imagine if you added some great graphics or video clips to give your posts more, "pop"!
    Your content is excellent but with pics and video clips,
    this website could certainly be one of the best in its niche.
    Fantastic blog!

    Review my web-site :: xn--Kxadbjpsnyt5A.com

    ReplyDelete
  28. Excellent post. I was checking continuously this blog and I am impressed!
    Very useful information specifically the last part :) I
    care for such info a lot. I was looking for this particular information
    for a long time. Thank you and best of luck.

    Here is my blog; www.gamestv.org

    ReplyDelete
  29. Pretty portion of content. I simply stumbled upon your weblog and
    in accession capital to claim that I acquire actually enjoyed account your
    blog posts. Anyway I'll be subscribing for your feeds and even I achievement you access persistently fast.

    Feel free to surf to my page :: free live web sex cam

    ReplyDelete
  30. I like what you guys are up too. Such clever work and coverage!
    Keep up the great works guys I've included you guys to blogroll.

    Here is my web page: efektywnie.Com

    ReplyDelete
  31. I feel that is one of the most important info for me.
    And i am satisfied reading your article. But want to observation
    on few normal things, The site taste is ideal, the articles is in point of
    fact nice : D. Good process, cheers

    Also visit my page - polyvore.com

    ReplyDelete
  32. What i don't realize is actually how you're not actually a lot more well-liked than you might be now.

    You're very intelligent. You understand therefore considerably with regards to this subject, produced me in my opinion imagine it from so many numerous angles. Its like men and women are not fascinated until it is something to accomplish with Woman gaga! Your individual stuffs outstanding. At all times care for it up!

    my web site: http://photopeach.com/user/flag8pen

    ReplyDelete
  33. Good day very nice site!! Guy .. Excellent .. Superb .
    . I'll bookmark your site and take the feeds also? I'm happy
    to find numerous useful info right here in the submit, we want develop more techniques in this regard,
    thanks for sharing. . . . . .

    My website; online adult cams

    ReplyDelete
  34. Having read this I thought it was really enlightening.
    I appreciate you finding the time and energy to put this informative article
    together. I once again find myself personally spending way too much time
    both reading and leaving comments. But so what, it was still
    worth it!

    Also visit my blog post: nude live sex cams

    ReplyDelete
  35. I just like the valuable information you supply to your articles.
    I'll bookmark your blog and test again here frequently. I'm moderately
    certain I will be told many new stuff proper here!
    Best of luck for the next!

    My web-site - free cam Sex

    ReplyDelete
  36. Great goods from you, man. I have have in mind your stuff prior to and you're simply extremely fantastic. I actually like what you have bought here, really like what you're saying
    and the best way by which you assert it. You make it enjoyable and you still take care of to keep it wise.
    I cant wait to learn far more from you. That is
    actually a terrific site.

    Here is my web-site: live Sex cam videos

    ReplyDelete
  37. This post gives clear idea in support of
    the new people of blogging, that in fact how to do blogging and
    site-building.

    Also visit my web site ... video chat sex free

    ReplyDelete
  38. Yes! Finally something about download porn star movie.


    My web-site ... jnmassage.info

    ReplyDelete
  39. Appreciate this post. Let me try it out.

    Check out my site porno frro

    ReplyDelete
  40. When I originally commented I clicked the "Notify me when new comments are added" checkbox
    and now each time a comment is added I get several emails with
    the same comment. Is there any way you can remove people from that service?
    Thanks!

    Also visit my homepage - live porn video for free

    ReplyDelete
  41. Hi there, its good post on the topic of media print,
    we all be aware of media is a impressive source of information.


    Here is my webpage; Tooring.Net

    ReplyDelete
  42. Wow, this piece of writing is fastidious, my sister is analyzing these kinds
    of things, thus I am going to tell her.

    my homepage ... dabagirls.com

    ReplyDelete
  43. This design is spectacular! You obviously know how to keep a reader
    entertained. Between your wit and your videos, I was almost moved to start my own
    blog (well, almost...HaHa!) Wonderful job. I really loved what you
    had to say, and more than that, how you presented it. Too
    cool!

    Here is my website - akibia.de

    ReplyDelete
  44. My partner and I absolutely love your blog and
    find nearly all of your post's to be exactly what I'm
    looking for. Do you offer guest writers to write content in your case?

    I wouldn't mind producing a post or elaborating on a few of the subjects you write in relation to here. Again, awesome blog!

    My web-site www.hummaa.com

    ReplyDelete
  45. Hey there, I think your site might be having browser compatibility issues.
    When I look at your blog site in Safari, it looks fine but when opening in
    Internet Explorer, it has some overlapping. I just wanted to give you
    a quick heads up! Other then that, wonderful blog!

    Take a look at my web-site free porn on movies (www.rennsouth.com)

    ReplyDelete
  46. However, there may be a diabeticsupport group, fibromyalgia; hypertension, arthritis, as well as groups
    of people with a common connection such as stay at home moms, working moms, bicyclist,
    hikers and so on. The milk is usually made from the same patented Real
    Feel Super Skin material that's made Fleshlight the #1 selling male sex toy during SXSW.

    ReplyDelete
  47. What's up to every body, it's my first go to see of this web site; this web site consists of remarkable
    and actually fine data in support of visitors.


    Also visit my web site ... cyber sex chat free (http://viavio.net/)

    ReplyDelete
  48. Hi, I read your new stuff like every week.
    Your writing style is awesome, keep up the good work!


    Feel free to visit my blog post - sex cam live
    for free ()

    ReplyDelete
  49. We are a group of volunteers and opening a new
    scheme in our community. Your website offered us with valuable information to work on.
    You've done an impressive job and our whole community will be thankful to you.

    my web site: live sex web

    ReplyDelete
  50. Hey there I am so delighted I found your web site,
    I really found you by accident, while I was looking on Digg for something else,
    Anyhow I am here now and would just like to say thanks a lot
    for a incredible post and a all round entertaining blog
    (I also love the theme/design), I don’t have time to look over it all
    at the moment but I have saved it and also added in your RSS feeds, so when I have time I will be
    back to read more, Please do keep up the fantastic work.


    Also visit my web blog: online sex cam **

    ReplyDelete
  51. I have been browsing online more than 3 hours lately,
    yet I by no means discovered any interesting article like yours.

    It's lovely value sufficient for me. In my opinion, if all website owners and bloggers made good content as you probably did, the web can be much more useful than ever before.

    My homepage ... adult webcam live - -

    ReplyDelete
  52. I simply couldn't depart your site before suggesting that I extremely loved the standard info a person provide on your guests? Is gonna be again steadily to check up on new posts

    My site: online webcam *fish-games.org*

    ReplyDelete
  53. You could definitely see your skills in the work you write.
    The sector hopes for even more passionate writers like
    you who are not afraid to say how they believe. All the time follow your
    heart.

    My homepage: cam model porn (http://mountain-topmusic.com)

    ReplyDelete
  54. continuously i used to read smaller articles that as well clear their motive, and that is also happening with
    this piece of writing which I am reading at this place.

    Look at my page: porn live shows

    ReplyDelete
  55. I don't even know how I ended up here, but I thought this post was good. I do not know who you are but certainly you are going to a famous blogger if you aren't already ;) Cheers!


    Have a look at my weblog: porn sites

    ReplyDelete
  56. It's amazing designed for me to have a web site, which is beneficial in favor of my experience. thanks admin

    My homepage ... live nude sex chat

    ReplyDelete
  57. This is my first time pay a visit at here and i am
    truly pleassant to read everthing at one
    place.

    Also visit my weblog - live sex porno :: ::

    ReplyDelete
  58. Tremendous issues here. I'm very satisfied to peer your article. Thank you a lot and I am taking a look forward to contact you. Will you kindly drop me a mail?

    My website ... live sexy webcam free

    ReplyDelete
  59. We are a group of volunteers and starting a
    new scheme in our community. Your site offered us with valuable info to work
    on. You've done an impressive job and our whole community will be thankful to you.

    my web site ... my free cams ()

    ReplyDelete
  60. No matter if some one searches for his vital thing, thus he/she wishes to be available that in detail, so that thing is maintained over here.


    Here is my weblog ... adult live sex cams (http://crosquare.com/)

    ReplyDelete
  61. I must thank you for the efforts you've put in writing this blog. I am hoping to view the same high-grade content from you in the future as well. In truth, your creative writing abilities has motivated me to get my own blog now ;)

    Also visit my website ... web live cam (meet2fun.com)

    ReplyDelete
  62. This information is invaluable. When can I find out more?



    Here is my blog; sexy chat live

    ReplyDelete
  63. Pretty part of content. I simply stumbled upon your website and in accession capital to say that
    I get in fact loved account your weblog posts.
    Any way I'll be subscribing in your feeds or even I success you get entry to consistently rapidly.

    Also visit my web blog: sex cams chat []

    ReplyDelete
  64. Nice post. I was checking continuously this blog and
    I'm impressed! Extremely helpful info specially the last part :) I take care of such info much. I used to be seeking this particular information for a long time. Thank you and best of luck.

    Here is my webpage sex chat videos free ()

    ReplyDelete
  65. Hi, Neat post. There's an issue along with your website in internet explorer, might test this? IE nonetheless is the market leader and a big component to other folks will pass over your fantastic writing due to this problem.

    My homepage: sex free cam

    ReplyDelete
  66. hey there and thank you for your info – I have definitely picked up something new from right here.
    I did however expertise several technical issues using this website,
    since I experienced to reload the site lots of times previous to I could get it to load properly.
    I had been wondering if your web hosting is OK?

    Not that I'm complaining, but slow loading instances times will often affect your placement in google and can damage your high-quality score if advertising and marketing with Adwords. Well I'm adding this RSS to my email and could look out for much more of your respective interesting
    content. Make sure you update this again soon.

    Also visit my blog post webcam chat adult (http://www.storenvy.com/walk08rule)

    ReplyDelete
  67. Good post! We will be linking to this great content on our website.

    Keep up the great writing.

    Visit my web blog Adult Live sex

    ReplyDelete
  68. Hi there! Do you use Twitter? I'd like to follow you if that would be okay. I'm definitely enjoying your blog and look forward to new posts.


    my blog post; sex chat free live (www.Screenwritersfederation.org)

    ReplyDelete