Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2006-02-03 06:54:50

LLoyd
Guest

### Quotation and Chain Rule HELP

Hi everybody, can you help me solve this:

y = (2x+1 / 3x-2)^5

find dy/dx using the quotation and chain rules.

ive got an answer but i think i got confussed during the quotation rule.

Thanks

## #2 2006-02-03 07:22:59

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Quotation and Chain Rule HELP

y′ = 5(2x+1 / 3x - 2)^4 * [ (3x-2)2 - (2x+1)3 ] / (3x-2)²
= 5(2x+1 / 3x - 2)^4 * -7 / (3x-2)²

El que pega primero pega dos veces.

Offline

## #3 2006-02-03 10:05:58

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Quotation and Chain Rule HELP

Yes, but could you imagine being given:

560x^4 + 1120x^3 + 840x^2 + 280x + 35
81x^4 - 216x^3 + 216x^2 - 96x + 16

And have to integrate it back to something resembling what we have above?!

Offline

## #4 2006-02-03 10:28:29

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Quotation and Chain Rule HELP

Can anyone say polynomial division?

El que pega primero pega dos veces.

Offline

## #5 2006-02-03 10:48:01

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Quotation and Chain Rule HELP

I certainly applaud you ryos, if you brave and energetic enough to do that sort of division on this equation.

Offline

## #6 2006-02-05 14:16:45

God
Member
Registered: 2005-08-25
Posts: 59

### Re: Quotation and Chain Rule HELP

0.03 seconds using the mathematica online integrator.

Offline

## #7 2006-02-06 11:37:26

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Quotation and Chain Rule HELP

Sorry, God.  I am an old guy and have a tendency to want to do things by hand.  Whenever I use my TI-89, I almost feel like I'm cheating in some way.  But if you really need an answer there is nothing wrong with using technology to find the answer.  Actually, I use my calculator all of the time, it's not like I sat down and memorized the trigonomic tables....hmm, I have to put that on my to-do list.

Offline

## #8 2006-02-06 15:34:22

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Quotation and Chain Rule HELP

it's not like I sat down and memorized the trigonomic tables....hmm, I have to put that on my to-do list.

Which is only second to memorizing The On-Line Encyclopedia of Integer Sequences
.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

## #9 2006-02-06 16:00:52

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Quotation and Chain Rule HELP

I didn't mean every fractional degree.  Just maybe every degree of sine up to forty-five for example.  You wouldn't have to do cosine or tangent because of the relationships among them.

A list of forty five numbers, to an accuracy of my choosing, wouldn't be that hard.  I memorized the first five hundred digits of pi over ten years ago and I can still write them down on a piece of paper if I had to.  There are many different ways to remember long numbers and lists, some techniques dating back to ancient Greece.  Ironically, they don't bother teaching these techniques to school children.

Offline