1. #1
    Banned sandmoth12's Avatar
    Join Date
    Aug 2011
    Location
    California
    Posts
    1,767

    Exclamation Help with a math problem.

    I need to find the derivative of sin^5(cos(6x))

    It is a homework problem, but I am really just wanting someone the order of how I should work this problem.

  2. #2
    I cba to do this myself, so here's a nice page for you:

    http://www.wolframalpha.com/input/?i...cos%286x%29%29

    It should show the solution as well.

  3. #3
    Banned sandmoth12's Avatar
    Join Date
    Aug 2011
    Location
    California
    Posts
    1,767
    Quote Originally Posted by vanin View Post
    I cba to do this myself, so here's a nice page for you:

    http://www.wolframalpha.com/input/?i...cos%286x%29%29

    It should show the solution as well.
    I don't want just the solution, that's easy and cheating. I want to know how to do this problem.

  4. #4
    I am Murloc! Raiju's Avatar
    Join Date
    Apr 2011
    Location
    England
    Posts
    5,810
    Quote Originally Posted by sandmoth12 View Post
    I don't want just the solution, that's easy and cheating. I want to know how to do this problem.
    I want to be able to explain to my teacher how "I" did this problem*.

  5. #5
    Banned sandmoth12's Avatar
    Join Date
    Aug 2011
    Location
    California
    Posts
    1,767
    Quote Originally Posted by Raiju View Post
    I want to be able to explain to my teacher how "I" did this problem*.
    No, I want to be able to explain to my teacher how this problem would be done.

  6. #6
    I am Murloc! Raiju's Avatar
    Join Date
    Apr 2011
    Location
    England
    Posts
    5,810
    ...Isn't that what they're meant to teach you and what you listen to in class? And take notes?

  7. #7
    The Patient
    Join Date
    Nov 2010
    Location
    The United Kingdom of Great Britain and Northern Ireland
    Posts
    336
    Quote Originally Posted by sandmoth12 View Post
    No, I want to be able to explain to my teacher how this problem would be done.
    If you click step-by-step solution you can see the entire proof.



    Gotta love a bit of chain rule.

  8. #8
    guess i was wrong :P heheh

  9. #9
    Legendary! vindicatorx's Avatar
    Join Date
    May 2009
    Location
    Bloomington, Indiana
    Posts
    6,443
    Quote Originally Posted by Raiju View Post
    ...Isn't that what they're meant to teach you and what you listen to in class? And take notes?
    I know right that was what I thought as well not here at my school they don't in most classes they don't even use text books so we can use the text to see how things are done they post some half ass notes they use where they don't show the work used to solve a problem they just show the answer and thats exactly what they do in class as well using the same examples.

  10. #10
    Legendary! Blueobelisk's Avatar
    Join Date
    May 2011
    Location
    New York
    Posts
    6,585
    Lol at that program. I was about to come in here and do a big explanation.

    Yeah, do the multiplication derivative rule.

  11. #11
    Chain rule is your friend!
    "Then we have found, as it seems, that the many beliefs of the many about what's fair and about the other things roll around somewhere between not-being and being purely and simply." - Plato: Republic

  12. #12
    I am Murloc! Raiju's Avatar
    Join Date
    Apr 2011
    Location
    England
    Posts
    5,810
    Quote Originally Posted by vindicatorx View Post
    I know right that was what I thought as well not here at my school they don't in most classes they don't even use text books so we can use the text to see how things are done they post some half ass notes they use where they don't show the work used to solve a problem they just show the answer and thats exactly what they do in class as well using the same examples.
    Had trouble understanding but the gist is you don't actually get taught? That's pretty bad. I did this on a course a couple years ago and if you didn't understand the admittedly rushed and brief in lesson content you could get support sessions with the teacher outside of class time where you were both free (usually lunch times and such), and we had a book for reference which did have everything in it if you needed to cover something. Teachers also printed off their presentations and encouraged you to take notes.

  13. #13
    Herald of the Titans
    Join Date
    Apr 2010
    Location
    Vineland, Cumberland, NJ, USA
    Posts
    2,593
    Quote Originally Posted by sandmoth12 View Post
    I need to find the derivative of sin^5(cos(6x))

    It is a homework problem, but I am really just wanting someone the order of how I should work this problem.
    You have to do Chain rule a few times. Chain rule: I'O'(I), where I is the inside function and O is the outside function. But you have multiple functions.
    Going from furthest out to furthest in: x^5 ; sin(x) ; cos(x) ; 6x
    5(sin(cos(6x))^4*Dx(sin(cos(6x))
    =5(sin(cos(6x))^4*cos(cos(6x))*Dx(cos(6x))
    =5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*Dx(6x)
    =5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*6
    Bring all coeffiecients to the front:
    =-30[sin(cos(6x))^4*cos(cos(6x))*sin(6x)]

    EDIT: Woohoo someone posted WolframAlpha doing the same thing

  14. #14
    Quote Originally Posted by Linkedblade View Post
    You have to do Chain rule a few times. Chain rule: I'O'(I), where I is the inside function and O is the outside function. But you have multiple functions.
    Going from furthest out to furthest in: x^5 ; sin(x) ; cos(x) ; 6x
    5(sin(cos(6x))^4*Dx(sin(cos(6x))
    =5(sin(cos(6x))^4*cos(cos(6x))*Dx(cos(6x))
    =5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*Dx(6x)
    =5(sin(cos(6x))^4*cos(cos(6x))*-sin(6x)*6
    Bring all coeffiecients to the front:
    =-30[sin(cos(6x))^4*cos(cos(6x))*sin(6x)]

    EDIT: Woohoo someone posted WolframAlpha doing the same thing
    Damn, beat me to it.

    Anyways, like everyone said, it's all chain rule. The trick is to figure out how many times you need to apply it.
    You need to apply it once for the power outside the original sin function, once for the actual sin function, once for the cos function inside the sin function, and then finally you need to find the derivative of 6x inside last cos function.

    It's basically a problem testing to see if you understand chain rule.

  15. #15
    Herald of the Titans theredviola's Avatar
    Join Date
    Jul 2008
    Location
    Arkansas
    Posts
    2,731
    Quote Originally Posted by Raiju View Post
    ...Isn't that what they're meant to teach you and what you listen to in class? And take notes?
    Just because a teacher teaches it once doesn't mean everyone understood. On a good day, I teach by a 80/20 rule. If 80% of what I taught was absorbed, then it's successful. The other 20% need to be retaught, or taught in a different way for them to be a success. Every student CAN learn. It's a teacher's job to find which way speaks to which student. Sadly, though, some students are simply to lazy and refuse to do the work -- making it appear they didn't learn the material.

    For some students simply "listening" isn't enough. Some have to work through it a few times, others have to try it from another approach. This is especially important in math. I didn't understand most any math I had in grade school. I didn't get it until I took the general ed math class in college when I had a prof who gave us links to websites that would explain 10 different ways to do different equations so that we could find what works best for us.
    "Do not only practice your art, but force yourself into its secrets, for it and knowledge can raise men to the divine." -- Ludwig Van Beethoven

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •