# Diffrentiation...Watch

Thread starter 10 years ago
#1
x=3(cos^2)t

I'm utterly confused. When do you know to use [cos2t=2cos^2-1]?
Can it be done both ways?

MS:6cost x (-sint)

Eh?
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10 years ago
#2
differentiating (cos^2t) gives (2cos t)(-sin t)
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10 years ago
#3
If it helps, i think 3(cos^2)t is the same as 3(cost)^2...
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10 years ago
#4
You could do it using double angle formulae, but it's a lot of work for what's essentially a very simple calculation. I would stick to using the chain rule on .
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10 years ago
#5
I'm afraid I didn't get your point. You can do what both ways? If you mean between cos^2t and cos2t, then yes in differentiation, standard differentiation rules could be used on trig functions, but not in integration. and yes your answer is right
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Thread starter 10 years ago
#6
This is the result of revising C4 without C3. Thanks!
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Thread starter 10 years ago
#7
New question....

Integrating x/(x+1)

Using the quotient rule I'm getting x+1-x/(x+1)^2 but the book claims x+1-1/(x+1)

How is it getting this value?
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10 years ago
#8
(Original post by Tombola)
New question....

Integrating x/(x+1)

Using the quotient rule I'm getting x+1-x/(x+1)^2 but the book claims x+1-1/(x+1)

How is it getting this value?
integrating?

well x/(x+1) = 1 - 1/(x+1)

int 1 - 1/(x+1) = x - ln|x+1| + C
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Thread starter 10 years ago
#9
Yeah... I'm sort of lost on where you got the first part from.

What rule did you use?
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10 years ago
#10
(Original post by Tombola)
Yeah... I'm sort of lost on where you got the first part from.

What rule did you use?
This is integration right? It's not really a rule

x/(x+1) = (x+1)/(x+1) - 1/(x+1) = 1 - 1/(x+1)?

Then x - ln(x+1)
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Thread starter 10 years ago
#11
My bad. I meant I don't really understand how/why to get from x/(x+1) to (x+1)/(x+1) - 1/(x+1)
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10 years ago
#12
A slightly longer way is to make the substitution u = x + 1 and split the fraction.
10 years ago
#13
(Original post by Tombola)
Yeah... I'm sort of lost on where you got the first part from.

What rule did you use?
Try not to think of them as inflexible rules. Just use GCSE level rules to manipulate the fraction into something easily integrable.

(I think I showed the x - ln(x+1) above.
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Thread starter 10 years ago
#14
Thanks.
It's probably something very easy but it's not coming to me naturally. I'll recall how to manipulate the fraction in a while.
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10 years ago
#15
(Original post by Tombola)
Thanks.
It's probably something very easy but it's not coming to me naturally. I'll recall how to manipulate the fraction in a while.
any other questinos before i head off?
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10 years ago
#16
you can work out by partial fractions from that\
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Thread starter 10 years ago
#17
(Original post by n1r4v)
any other questinos before i head off?
Nope! Much appreciated for your help Thanks!

Should be fine with the more complicated stuff.
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Thread starter 10 years ago
#18
Hi.

I'm trying to diffrentiate so I get but diffrentiating that would give me sin2t.

I'm clearly wrong but I'm just wondering why I can't do it via that method.
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10 years ago
#19
(Original post by Tombola)
Hi.

I'm trying to diffrentiate so I get but diffrentiating that would give me sin2t.

I'm clearly wrong but I'm just wondering why I can't do it via that method.
What you've done is right. What makes you think it isn't?
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Thread starter 10 years ago
#20
(Original post by Daniel Freedman)
What you've done is right. What makes you think it isn't?
Using the chain rule would give me a different answer.

4Sintcost... Oh right. Sin2t = 4sintcost.

Okay thanks. I forgot about the last step.
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