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# Stuck on an FP2 question!

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1. I understand how to do it for say y = (tan(1+x)^-1) but this fraction is really throwing me off... any advice?
2. (Original post by 2014_GCSE)

I understand how to do it for say y = (tan(1+x)^-1) but this fraction is really throwing me off... any advice?
2014 AQA right? Anyway, just approach it as normal, it falls out nicely (From memory at least)
3. write f(x) = tan(y)

make x the subject, then find dx/dy.... after that you can get dy/dx easily.
4. In the first part you have shown that

So now just solve the differential equation giving .
y is defined above as so substitute that in for y. Then find c as you normally would and rearrange to give the required result.
^ for the second part of the question.

For the first part just use chain rule (you will need quotient rule as well when differentiating the fraction).
5. Thanks, zetamcfc, the bear and B_9710. I managed to get part a) with what you guys said but still struggling with part b). I even just had a look at the mark scheme and I still am not really understanding b)...

For the post above, where have you pulled the equation "y=arctanx + c" from? I understand it may give you the answer but I don't understand the logical steps?
6. (Original post by 2014_GCSE)
Thanks, zetamcfc, the bear and B_9710. I managed to get part a) with what you guys said but still struggling with part b). I even just had a look at the mark scheme and I still am not really understanding b)...

For the post above, where have you pulled the equation "y=arctanx + c" from? I understand it may give you the answer but I don't understand the logical steps?
What's part b?
7. (Original post by Kvothe the arcane)
What's part b?
Sorry, I didn't realise the photo didn't have the letters in there. Part b) is "Hence, given that x<1... etc."
8. (Original post by 2014_GCSE)
Sorry, I didn't realise the photo didn't have the letters in there. Part b) is "Hence, given that x<1... etc."
We need to know what ...etc is

Edit: stupid me
9. (Original post by 2014_GCSE)
Sorry, I didn't realise the photo didn't have the letters in there. Part b) is "Hence, given that x<1... etc."
Integrate your dy/dx, what do you see?
10. (Original post by 2014_GCSE)
Thanks, zetamcfc, the bear and B_9710. I managed to get part a) with what you guys said but still struggling with part b). I even just had a look at the mark scheme and I still am not really understanding b)...

For the post above, where have you pulled the equation "y=arctanx + c" from? I understand it may give you the answer but I don't understand the logical steps?
It comes from solving the differential equation .
And remember that .
11. Ah, of course. Got it!! Thanks everybody

(Original post by Kvothe the arcane)
We need to know what ...etc is
I put the question in the OP
12. (Original post by 2014_GCSE)
Ah, of course. Got it!! Thanks everybody

I put the question in the OP
I wouldn't do it the way that the other users have, I'd write , then from the first part, notice that:

So that . Then .
13. (Original post by Zacken)
I wouldn't do it the way that the other users have, I'd write , then from the first part, notice that:

So that . Then .
STEP I question there?
14. (Original post by Zacken)
I wouldn't do it the way that the other users have, I'd write , then from the first part, notice that:

So that . Then .
Why would you know that ?

I assume you're not used that fact as that'd be circular reasoning.
15. (Original post by Kvothe the arcane)
Why would you know that ?

I assume you're not used that fact as that'd be circular reasoning.
Because and .

Derivative is a linear operator so since you're differentiating the difference of two things whose derivatives are the same, then . So is a constant and plugging in any value of will reveal the value of this constant.
16. (Original post by B_9710)
STEP I question there?
First part of a STEP I question from a paper in the 80's or 90's iirc.
17. (Original post by Zacken)
Because and .

Derivative is a linear operator so since you're differentiating the difference of two things whose derivatives are the same, then . So is a constant and plugging in any value of will reveal the value of this constant.
That was stupid of me. Didn't notice they were the same. Thanks. Noted.
18. (Original post by Kvothe the arcane)
That was stupid of me. Didn't notice they were the same. Thanks. Noted.
I think that was the intended solution as well - they gave you part (a) to show the derivative of that is the derivative of too. It's a nice concept.
19. (Original post by Zacken)
I think that was the intended solution as well - they gave you part (a) to show the derivative of that is the derivative of too. It's a nice concept.
http://filestore.aqa.org.uk/subjects...W-MS-JUN14.PDF

Q7 if you want the desired solution
20. (Original post by zetamcfc)
http://filestore.aqa.org.uk/subjects...W-MS-JUN14.PDF

Q7 if you want the desired solution
Thanks for setting me straight.

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