Diffrentiation... Watch

Tombola
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#1
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#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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hermaphrodite
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#2
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differentiating (cos^2t) gives (2cos t)(-sin t)
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LLGJ x
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#3
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If it helps, i think 3(cos^2)t is the same as 3(cost)^2...
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Adjective
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#4
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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 \displaystyle \frac{d}{dt} 3(\cos t)^2 .
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pisces_abhi
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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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Tombola
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This is the result of revising C4 without C3. Thanks!
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Tombola
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#7
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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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Cities
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(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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Tombola
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Yeah... I'm sort of lost on where you got the first part from.

What rule did you use?
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Cities
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(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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Tombola
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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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Glutamic Acid
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A slightly longer way is to make the substitution u = x + 1 and split the fraction.
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Cities
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(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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Tombola
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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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Cities
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(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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Goldenratio
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\displaystyle \frac{x}{x+1}=\frac{x+1-1}{x+1}=\frac{A}{x+1}+1 you can work out by partial fractions from that\
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Tombola
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(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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Tombola
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#18
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Hi.

I'm trying to diffrentiate y = 2sin^{2}t so I get y = 1 - cos2t 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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Daniel Freedman
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(Original post by Tombola)
Hi.

I'm trying to diffrentiate y = 2sin^{2}t so I get y = 1 - cos2t 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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Tombola
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#20
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(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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