You are Here: Home >< Maths

# C4 Differentiation, I keep checking over my work yet I cannot find my mistake. :( watch

1. Question: x= 2t/1+(t^2) y= 1 - (t^2)/1 + (t^2)

btw is 1 + (t^2) the same as (1+t^2)?

for x' i got: 2-2t/(1+t^3)
for y' i got: -4(1+t^2)/(1+t^3)

they must be wrong, right? I cant get the right answer for dy/dx.

By the quotient rule, for x i got: 2-2t/1+t^4 and for y i got: 4t^3/1+t^4

arghhhhhhhhhhhhh
2. Shouldn't the bottom line of your x be (1 + t^2) ^2?

Using the quotient rule the bottom line = v^2, v = 1+ t^2, I can't see how you managed to get 1+ t^3. You should also have 2 - 2t^2 on the top. I'm thinking maybe you tried to simplify but you can't really do that in the way you seem to have done it.
3. dx/dt= 2(1-t^2)/(1+t^2)^2

dy/dt= -4t/(1+t^2)^2

dy/dx= -t/(1-t^2)
4. (Original post by You Failed)
Shouldn't the bottom line of your x be (1 + t^2) ^2?

Using the quotient rule the bottom line = v^2, v = 1+ t^2, I can't see how you managed to get 1+ t^3.
I used the product rule and got a completely different answer to when I used the quotient rule. My quotient rule answers are posted above
5. (Original post by Sakujo)
dx/dt= 2(1-t^2)/(1+t^2)^2

dy/dt= -4t/(1+t^2)^2

dy/dx= -t/(1-t^2)
That's wrong, it's 2t/t^2 - 1
6. (Original post by Get Cape.Wear Cape.Fly.)

By the quotient rule, for x i got: 2-2t/1+t^4 and for y i got: 4t^3/1+t^4

arghhhhhhhhhhhhh
Thw whole of the denominator is squared so it's (1+t^2)^2 not 1+t^4.
7. (Original post by Get Cape.Wear Cape.Fly.)
That's wrong, it's 2t/t^2 - 1
It should be 2t on top but otherwise it's right.
8. (Original post by Sakujo)
It should be 2t on top but otherwise it's right.
How is it right when your denominator is different?
9. (Original post by Get Cape.Wear Cape.Fly.)
I used the product rule and got a completely different answer to when I used the quotient rule. My quotient rule answers are posted above
Your simplification of the bottom line is wrong. It's (1 + t^2) ALL squared, which is (1 + t^2)(1+ t^2), this doesn't just simplify to 1 + t^4. Maybe this will help in some way =P I can't actually be bothered to work the whole way through the question, I'm procrastinating from my own work at the moment lol.
10. I'm on the verge of jumping off a bridge.
11. Ok, for x

u = 2t
u' = 2

v= 1+t^2
v'= 2t

??????????????

i think my v' is wrong? omg help!
12. amirite?
13. (Original post by Get Cape.Wear Cape.Fly.)
Ok, for x

u = 2t
u' = 2

v= 1+t^2
v'= 2t

??????????????

i think my v' is wrong? omg help!
It's not wrong.
14. (Original post by antonfigo)
amirite?
How do you get from -2t/1-t^2 to 2t/1-t^2? do you multiply by -1?

Your working is exactly what I got (amongst the mess on my notepad)...
15. (Original post by Get Cape.Wear Cape.Fly.)
How is it right when your denominator is different?
If you times what I wrote before by minus one you should get the correct denominator.
16. Why does it go all wrong when I differentiate by product rule......
17. (Original post by Get Cape.Wear Cape.Fly.)
Why does it go all wrong when I differentiate by product rule......
It ALWAYS goes wrong when you use product rule for fractions....
I've tried that loads of time and it becomes too complex with the ^-1 s and whatnot...

18. (Original post by antonfigo)
It ALWAYS goes wrong when you use product rule for fractions....
I've tried that loads of time and it becomes too complex with the ^-1 s and whatnot...

That is the biggest load of rubbish I have read on TSR in months. You do know that the quotient rule is just a special case of the product rule?

(Original post by Get Cape.Wear Cape.Fly.)
Why does it go all wrong when I differentiate by product rule......
Hmm, when you have then to differentiate that you need to use the chain rule, i.e. differentiate the outside and times it by the differentiate of the inside. You are doing that wrong.
19. (Original post by Simplicity)
That is the biggest load of rubbish I have read on TSR in months. You do know that the quotient rule is just a special case of the product rule?

Hmm, when you have then to differentiate that you need to use the chain rule, i.e. differentiate the outside and times it by the differentiate of the inside. You are doing that wrong.
I didnt mean it literally :P
What I was trying to say was that if you try the quotient rule (quite tempting! i say from experience) during an exam with the question presenting a complex fraction with logs etc,you are bound to make a mistake somewhere after when it becomes complex enough ( i got one of those in a term paper)...unless you are really really good...don't try it at exam
20. (Original post by antonfigo)
I didnt mean it literally :P
What I was trying to say was that if you try the quotient rule (quite tempting! i say from experience) during an exam with the question presenting a complex fraction with logs etc,you are bound to make a mistake somewhere after when it becomes complex enough ( i got one of those in a term paper)...unless you are really really good...don't try it at exam
I disagree again. Certainly, the product rule is more intuitive and therefore better. Anyway, if you aren't a robot you can see thats its basically the same, except you use the chain rule.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 6, 2010
Today on TSR

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams