1. Jan 20, 2009

prime-factor

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. Jan 20, 2009

NoMoreExams

Why would you use x as multiplication when it's your variable...

3. Jan 20, 2009

prime-factor

Sorry
I'll know not to next time.
Thankyou

4. Jan 20, 2009

NoMoreExams

5. Jan 20, 2009

prime-factor

Thanks.

6. Jan 20, 2009

NoMoreExams

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.

7. Jan 20, 2009

prime-factor

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 . 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?

8. Jan 20, 2009

NoMoreExams

You should probably attempt it, there's a pretty basic u-subst. for this one

9. Jan 20, 2009

Dick

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.

10. Jan 20, 2009

NoMoreExams

That may be true but this is a pretty simple integral :)

11. Jan 20, 2009

prime-factor

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!

12. Jan 20, 2009

Dick

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.

13. Jan 20, 2009

Dick

Right you are.

14. Jan 20, 2009

NoMoreExams

I can't speak to that, I've always done it both ways (then again I always had Maple to check my answers also).

15. Jan 20, 2009

Dick

That is a factor. But why not just use Maple to differentiate it then?

16. Jan 20, 2009

prime-factor

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
17. Jan 20, 2009

NoMoreExams

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

18. Jan 20, 2009

Dick

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?

19. Jan 20, 2009

prime-factor

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.

20. Jan 20, 2009

Dick

You will do so fine.