Product Rule Differentiation

OP

Ok, so I tried the questions again and I actually got the answer to (D) this time round. I discovered that I was applying the chain rule correctly. With (C), I'm still quite stuck. Here is what I've done so far in the picture below:

*Also, can I ask about Core 3 compared to Core 4? I actually found Core 2 easier than Core 1 and Statistics 2 easier than Statistics 1.

Original post by pprobson92

Ok, so I tried the questions again and I actually got the answer to (D) this time round. I discovered that I was applying the chain rule correctly. With (C), I'm still quite stuck. Here is what I've done so far in the picture below:

*Also, can I ask about Core 3 compared to Core 4? I actually found Core 2 easier than Core 1 and Statistics 2 easier than Statistics 1.

Right, so I agree with

\frac{dy}{dx} = 2x(x+1)^2 + 2(x^2-1)(x+1)

.

You've factorised out a

2(x+1)

term out which should get you

2(x+1)\bigg(x(x+1) + (x^2 - 1)\bigg)

- you're missing the

x

in the first term.

In regards to your second question, I'm not entirely sure. I found pretty much all the core units to be of a similar difficulty.

Reply 4

OP

Thank you. I appreciate your help. With your assistance, I got to the right answer and realised where I was going wrong. I saw the little trick with factoring the expanded quadratic equation at the end.

From now on, I will post pictures of both the question and my working to show you what I'm thinking. I may be doing this a fair bit though. Apologies in advance!

AS was actually pretty easy to self-teach, A2 is far more tricky.

Reply 5

Original post by pprobson92

Thank you. I appreciate your help. With your assistance, I got to the right answer and realised where I was going wrong. I saw the little trick with factoring the expanded quadratic equation at the end.

Great!

From now on, I will post pictures of both the question and my working to show you what I'm thinking. I may be doing this a fair bit though. Apologies in advance!

Yes, that's be lovely. Thank you. And don't worry about asking questions, nobody minds. :smile:

AS was actually pretty easy to self-teach, A2 is far more tricky.

I self-taught both and didn't think there was much of a difference but that's probably an odd opinion.

Reply 6

OP

Thank you. Ah ok, well each to their own. For me, I would definitely say there were varying degrees of difficulty between the modules, but that's how I feel.

Just out of curiosity, how did you fair grades wise with the self-taught maths A level? (don't have to say if you rather not) and which exam board were you with?

Reply 7

Original post by pprobson92

Thank you. Ah ok, well each to their own. For me, I would definitely say there were varying degrees of difficulty between the modules, but that's how I feel.

Just out of curiosity, how did you fair grades wise with the self-taught maths A level? (don't have to say if you rather not) and which exam board were you with?

I did it with Edexcel, ended up with:

Spoiler

How are you faring with the self-teaching? Are you with Edexcel as well?

Reply 8

OP

Wow, that's incredible. Well done! Do you have any secrets for success you could share? lol. I doubt I could marks like that, although at the same time, I don't see why not if I approach my learning in a certain way and put the effort in.

Core 1, 2, Statistics 1 and 2 - absolutely fine (I really like statistics and find it generally not very hard). Core 3 is very difficult. I've actually studied it before and am just recapping stuff now. Core 4 i enjoy.

Some topics I really enjoy, so I like Trigonometry but not range, domain and that type of maths.

Reply 9

Original post by pprobson92

Wow, that's incredible. Well done! Do you have any secrets for success you could share? lol. I doubt I could marks like that, although at the same time, I don't see why not if I approach my learning in a certain way and put the effort in.

Thank you! I don't see why you can't do it either if you put the work in.

Core 1, 2, Statistics 1 and 2 - absolutely fine (I really like statistics and find it generally not very hard). Core 3 is very difficult. I've actually studied it before and am just recapping stuff now. Core 4 i enjoy.

S2 is quite enjoyable (although we have rather differing opinions to the general populace) - I'm taking S3 currently and it's not as much fun as S2, although bits of it is rather more enjoyable. Looks like you just need to focus on C3 for a while and you're set to do excellently.

Some topics I really enjoy, so I like Trigonometry but not range, domain and that type of maths.

Hmm, yeah. You might want to look at this: Post 1 and Post 2 for some of the domain/range stuff that I've ranted on about previously, you might find it helpful!

Reply 10

OP

haha yeah, I think most people really don't enjoy statistics, but S2 was great. I think I covered everything in like 3 weeks and that wasn't even doing it full time as well. I had to take a stats course in my degree so that helped to an extent I think (albeit like 4 years ago I did that).

I wouldn't mind looking at S3. Further Maths actually sounds quite fun in a way.

Thank you, I hope to do well. I'm a bit low on the confidence side sometimes I think, but I enjoy Maths and just persevere through it. Just wanted to ask how come you self-taught the A level? Was it not something you wanted to do in 6th form/college?

Reply 11

Original post by pprobson92

../

Ah well, good luck to you!

Thank you, I hope to do well. I'm a bit low on the confidence side sometimes I think, but I enjoy Maths and just persevere through it. Just wanted to ask how come you self-taught the A level? Was it not something you wanted to do in 6th form/college?

It's a bit of a long story, see here in lieu of me repeating myself. :tongue:

What's your story? (if you don't mind me asking)

Reply 12

The-Spartan

6

Original post by pprobson92

*Also, can I ask about Core 3 compared to Core 4? I actually found Core 2 easier than Core 1 and Statistics 2 easier than Statistics 1.

An unpopular opinion but i find Core 3 slightly harder than Core 4. I find that C4 does more hand holding than C3. C3 also has proof, and does not have partial fractions which are free marks. C4 also has binomial expansion, which is also free marks. C3 is a calculus-fest :biggrin:

I found C1 harder than C2 last year :smile:

Good luck with your studies :yes:

Reply 13

OP

That's interesting to know. I suppose I wouldn't know in comparison to Core 4 (not yet anyway), but it feels like Core 3 really does throw you out there on your own. I gave up studying A2 maths for a long time because I just couldn't get the answer, no matter how much I tried when doing Core 3. It's a whole new level of maths as well I think.

Stories of Core 4 concern me a bit. I know a girl who got an A in each of the 5 units prior to Core 4 and only needed a D on Core 4 to get an A. She got a U and then ended up with a B overall. I'm not quite sure what happened with her tbh.

Thank you for your kind wishes :-)

Reply 14

OP

It's a bit of a long story, see here in lieu of me repeating myself. :tongue:

What's your story? (if you don't mind me asking)

Thank you, i'll have a read of your story in a minute. I basically gave up studying A Level Maths at school. I hated the teachers, the classes and the atmosphere. They didn't want to help us and even at one point told us that we didn't have text books because 'they got lost in the post'. I think most people got an E for AS. This would have also held me back for applying to uni degrees too.

I also don't really get on with maths in a classroom environment. I think I find it too pressurised which ends up with me getting the wrong answer. I self taught most of my GCSE and ended up with an A* in the exams, so I thought I could do it for A level. I like just working out of a text book.

I'm working through getting my A level now (at 23) because I'm doing my masters in Economics soon and actually may need the A level qualification for some careers in future.

Reply 15

Thank you, i'll have a read of your story in a minute. I basically gave up studying A Level Maths at school. I hated the teachers, the classes and the atmosphere. They didn't want to help us and even at one point told us that we didn't have text books because 'they got lost in the post'. I think most people got an E for AS. This would have also held me back for applying to uni degrees too.

I also don't really get on with maths in a classroom environment. I think I find it too pressurised which ends up with me getting the wrong answer. I self taught most of my GCSE and ended up with an A* in the exams, so I thought I could do it for A level. I like just working out of a text book.

I'm working through getting my A level now (at 23) because I'm doing my masters in Economics soon and actually may need the A level qualification for some careers in future.

Woah, that's admirable! Best of luck with it. :smile:

I totally understand not getting on with maths in a classroom environment, I feel much the same. Just make sure that you don't use the textbook as your only guide, try experimenting and playing around a bit with the maths you learn, ask yourself questions and see if you can stretch yourself; you'll be surprised at how flexible maths is and how fun it can be when you do that. Try not to rely single-handedly on the textbook only, but certainly use it as an aide.

Reply 16

OP

Apologies that this is such a bad photo. I can always re-write it and then upload a better photo.

I've basically been asked to integrate 'tanx' with 'pi/3' and 'o' as the limits.

I want to know why we get the answer we do when it comes to subtracting 'ln'. Why do the negative signs disappear and why do we switch around (or appear to switch around) the values of ln?

My text book doesn't explain this, so any help would be great.

Thank you.

IMG_0101.jpg496.0KB

Reply 17

7rance

Original post by pprobson92

Apologies that this is such a bad photo. I can always re-write it and then upload a better photo.

I've basically been asked to integrate 'tanx' with 'pi/3' and 'o' as the limits.

I want to know why we get the answer we do when it comes to subtracting 'ln'. Why do the negative signs disappear and why do we switch around (or appear to switch around) the values of ln?

My text book doesn't explain this, so any help would be great.

Thank you.

You can take the ' - ' in -ln(1/2) and raise (1/2) to it.
-ln(1/2) would become ln(1/2)^-1
(1/2)^-1 is the same as 1 / (1/2) ----> 2
So you end up writing it as ln 2.

Likewise for - ln (1),
(1)^-1 = 1 and ln 1 is always equal to 0.

So you're left with ln 2 - 0 = ln 2.

(edited 7 years ago)

Reply 18

OP