Math Is Fun Forum

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

You are not logged in.

#1 2006-01-17 08:06:04

simone
Guest

diffrentiation

How do i answer this question.............



Please HELP


    ln ((x + 1)(x + 2))²

to an accuracy of  3 decimal places if x = 0.5

#2 2006-01-17 09:29:15

irspow
Member
Registered: 2005-11-24
Posts: 1,055

Re: diffrentiation

Are you saying that you can't use a calculator?  If you can, it is easy.

The problem just says to take the natural log of [(x+1)(x+2)]²

Plug in the .5 they gave you and you get;

ln[(1.5)(2.5)] = ln(3.75) :asmp 1.321....

  If you are not allowed to use a calculator then one of the geniuses who spend time here will come up with a function for you later.


I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Offline

#3 2006-01-17 12:45:04

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: diffrentiation

The question is about differentiation so I assume you need to change ((x + 1)(x + 2))² into
((x + 1)(x + 2))*((x + 1)(x + 2)) = (x² + 3x + 2)*(x² + 3x + 2) = x^4 + 6x^3 + 4x^2 + 21x + 4

∫(x^4 + 6x^3 + 4x^2 + 21x + 4)dx = ...

or somthing like that?


Aloha Nui means Goodbye.

Offline

#4 2006-01-17 12:47:16

RickyOswaldIOW
Member
Registered: 2005-11-18
Posts: 212

Re: diffrentiation

∫dy/dx(x^4 + 6x^3 + 4x^2 + 21x + 4)dx = ∫4x^3 + 21x^2 + 8x + 21

Last edited by rickyoswaldiow (2006-01-17 12:47:35)


Aloha Nui means Goodbye.

Offline

#5 2006-01-17 13:06:46

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: diffrentiation

rickyoswaldiow has the right idea, but he's made a few minor errors.
The expansion is x[sup]4[/sup] + 6x³ + 13x² + 12x + 4
Differentiating that gives 4x³ + 18x² + 26x + 12

But there's an extra step because the whole thing is inside a big ln ( ).

This formula will help:

Using the values of f'(x) and f(x):

.

Someone else might be able to factorise the numerator for you.

Edit: Thanks, Ricky!

So that makes this your final answer:


Why did the vector cross the road?
It wanted to be normal.

Offline

#6 2006-01-17 13:22:10

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

Re: diffrentiation

Ti-89 to the rescue!

2(x+1)(x+2)(2x+3)


"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

#7 2006-01-17 13:30:20

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

Re: diffrentiation

Now, if you don't have access to a calculator, try to assume that x+1 is a factor.  If that doesn't work, try to assume x+2 is a factor.  Because if has any other factors, you don't really care about them.

If you know polynomial division, you can use this too.


"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

#8 2006-01-17 13:35:02

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

Re: diffrentiation

Last edited by Ricky (2006-01-17 14:04:23)


"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 2006-01-17 13:41:16

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: diffrentiation

I'm not sure if that's making it simpler or not. Either way, 2(2x) = 4x.


Why did the vector cross the road?
It wanted to be normal.

Offline

#10 2006-01-17 14:04:53

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

Re: diffrentiation

I think it does since you have to plug in and multiply less.


"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

#11 2006-01-17 15:00:40

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: diffrentiation

True point. If you had a value of x, you could probably work out f(x) quicker using that one.

Wow! We actually have a value of x. How did we miss that part?

Anyway, if x = 0.5, then f(x) = 2/1.5 - 2/2.5 = 4/3 - 4/5 = 20/15 - 12/15 = 8/15 = 0.533 to three decimal places.


Why did the vector cross the road?
It wanted to be normal.

Offline

#12 2007-05-17 00:52:41

harman
Guest

Re: diffrentiation

simone wrote:

How do i answer this question.............



Please HELP


    ln ((x + 1)(x + 2))²

to an accuracy of  3 decimal places if x = 0.5

ln ((x + 1)(x + 2))²
it is simple problem  man
firstly write it like this
f(x)=2ln(x+1)(x+2)
now diffrentiate it
f'(x)=2*[1/(x+1)(x+2)] *f'[(x+1)(x+2)]
f'(x)=2/(x+1)(x+2)*[(x+1)(1)+(x+2)(1)]
f'(x)=2(2x+3)/(x+1)(x+2)
this is the simple diffrentiation

the answer is same as suggested by mathsyperson moderater
now u can put ur value of x

#13 2008-05-15 23:31:33

shriyans
Guest

Re: diffrentiation

can any one help me diffrentiating:

z=sinx raised to power y .y raised to power x
y=log(to base 10)x
find dzy/dx and also d²z/dx²

#14 2008-05-16 05:10:41

Dragonshade
Member
Registered: 2008-01-16
Posts: 147

Re: diffrentiation

4x³ + 18x² + 26x + 12   there's a trick
4        8
         10        20
                     6      12

first write 4 and 12 at top left, and bottom right, then make every pair has the same ratio
(4x³+8x²) +.....

Last edited by Dragonshade (2008-05-16 05:11:48)

Offline

Board footer

Powered by FluxBB