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

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    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
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    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.
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    dx/dt= 2(1-t^2)/(1+t^2)^2

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

    dy/dx= -t/(1-t^2)
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    (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
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    (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
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    (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.
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    (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.
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    (Original post by Sakujo)
    It should be 2t on top but otherwise it's right.
    How is it right when your denominator is different?
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    (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.
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    I'm on the verge of jumping off a bridge.
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    Ok, for x

    u = 2t
    u' = 2

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

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

    i think my v' is wrong? omg help!
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    amirite?
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    (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.
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    (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)...
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    (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.:yep:
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    Why does it go all wrong when I differentiate by product rule......
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    (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...
    Use the quotient rule instead

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    (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...
    Use the quotient rule instead

    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 (1+x^2)^{-1} 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.
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    (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 (1+x^2)^{-1} 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
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    (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.
 
 
 
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