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Derivative please check my solution

  1. Jan 20, 2009 #1
    1. The problem statement, all variables and given/known data

    ln(cos5(3x4))


    2. Relevant equations

    chain rule:

    y = f(g(h)

    y' = f'(g(h) x g'(h) x h'


    3. The attempt at a solution

    y' = 1 / ((cos5(3x4)) x 5((cos4(3x4)) x -sin(3x4) x 12x3

    => -5sin(3x4)(12x3) / cos(3x4)

    => -60x3sin(3x4) / cos(3x4)

    => -60x3tan(3x4)

    =>No further simplification that I can see
     
  2. jcsd
  3. Jan 20, 2009 #2
    Why would you use x as multiplication when it's your variable...
     
  4. Jan 20, 2009 #3
    Sorry :redface:
    I'll know not to next time.
    Thankyou
     
  5. Jan 20, 2009 #4
    Maple confirms your answer :)
     
  6. Jan 20, 2009 #5
    Thanks.
     
  7. Jan 20, 2009 #6
    If you studied integrals you can always just integrate your answer and see if it's what you started with give or take a constant.
     
  8. Jan 20, 2009 #7
    I'm just starting to learn very basic integration before I start the school year. I would not know where to start integrating that solution to check at this stage:frown: . Would you be able to explain a good approach to integrating it? Or should I post it as a problem after I've attempted it?
     
  9. Jan 20, 2009 #8
    You should probably attempt it, there's a pretty basic u-subst. for this one
     
  10. Jan 20, 2009 #9

    Dick

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    I have NEVER heard anyone suggesting that you use integration to check a differentiation. The reverse, yes. Don't do it. Differentiation is easy. Integration is hard. Sometimes even when you know the answer. If you want integration practice go ahead, but it's not a practical check. You are much more likely to make a mistake in the integration than the differentiation.
     
  11. Jan 20, 2009 #10
    That may be true but this is a pretty simple integral :)
     
  12. Jan 20, 2009 #11
    Regardless. I am going to practice more integration and eventually (hopefully) master it successfully. It is already proving to need more problem-solving skills than derivatives!
     
  13. Jan 20, 2009 #12

    Dick

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    True, but then the differentiation isn't that hard either. I'm saying I don't recommend it as a general strategy. And I wouldn't worry the OP that being able to integrate is all that helpful in being able differentiate accurately.
     
  14. Jan 20, 2009 #13

    Dick

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    Right you are.
     
  15. Jan 20, 2009 #14
    I can't speak to that, I've always done it both ways (then again I always had Maple to check my answers also).
     
  16. Jan 20, 2009 #15

    Dick

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    That is a factor. But why not just use Maple to differentiate it then?
     
  17. Jan 20, 2009 #16
    You two seem two know what you're talking about so I'd like to ask this:

    I have a book by Kaplan and Lewis called: "Calculus and Linear Algebra [combined edition]. It is quite old (1970).

    Is that a good book in your opinion (assuming you know it or the authors works?
     
    Last edited: Jan 20, 2009
  18. Jan 20, 2009 #17
    Dick: because in my career sometimes I don't have the luxury of having Maple

    Prime-factor: I've never heard of it, I used Stewart to learn Calc. 1-3
     
  19. Jan 20, 2009 #18

    Dick

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    I don't know the book, either. Old ones aren't necessarily bad. Maple may be a luxury, but you don't need it. I went through my grad career using Mathematica. I was really quite hooked. Since I don't have people buying me CAS software anymore, I switched to Maxima. It's really pretty good. I can live with it. And it's FREE. But Prime-factor, if you do start using something like that, always make sure you know how to get the answer without the software, ok?
     
  20. Jan 20, 2009 #19
    No problem there. I'm a firm believer in practicing it 100 times if I don't get the answer before using a calculator. I've fallen into that trap once before and never again!. That's why I have plenty of Sharpies and A4 paper at my desk at all times, I do practice everything I learn, plus I'm starting year 12 this year with 2 Maths Subjects, so I've basically learnt the stuff I'll need for next year (except integration) in a couple of months from watching online tutorials and reading and hundreds of A4 pages of practice:P.
     
  21. Jan 20, 2009 #20

    Dick

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    You will do so fine.
     
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