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    Can anyone explain how you integrate 2^t, its from the January C4 paper? I'm stuck!
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    (Original post by twofatpigeons)
    Can anyone explain how you integrate 2^t, its from the January C4 paper? I'm stuck!
    How would you differentiate it?

    Use that knowledge to think of something that you could differentiate to give 2^t.
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    (Original post by fayled)
    How would you differentiate it?

    Use that knowledge to think of something that you could differentiate to give 2^t.
    I see how you do it now. Thanks for the tip
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    (Original post by twofatpigeons)
    Can anyone explain how you integrate 2^t, its from the January C4 paper? I'm stuck!
     y = 2^t

     lny = ln2^t

     lny = tln2

     \frac{dy}{dx} \frac{1}{y} = ln2

     \frac{dy}{dx} = yln2

    sub in  y = 2^t to get

     \frac{dy}{dx} = 2^tln2

    EDIT: sorry thought you said 'differentiate', to integrate all you do then is divide instead of times   \frac{2^t}{ln2}
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    (Original post by twofatpigeons)
    Can anyone explain how you integrate 2^t, its from the January C4 paper? I'm stuck!
    I used the substitution of u = 2^t and that got me the right answer in the end


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    (Original post by masryboy94)
     y = 2^t

     lny = ln2^t

     lny = tln2

     \frac{dy}{dx} \frac{1}{y} = ln2

     \frac{dy}{dx} = yln2

    sub in  y = 2^t to get

     \frac{dy}{dx} = 2^tln2
    Think you could do that by inspection to be fair...
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    (Original post by fayled)
    Think you could do that by inspection to be fair...
    This. A very wise thing to do.

    Just learn the fact that, to differentiate a^x, for any value of a or x, the differential is always a^xlna.

    But of course, if they ask you to prove it, do all the ninja business to do with rules of logs :ninja2:
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    (Original post by fayled)
    Think you could do that by inspection to be fair...
    (Original post by frogs r everywhere)
    This. A very wise thing to do.

    Just learn the fact that, to differentiate a^x, for any value of a or x, the differential is always a^xlna.

    But of course, if they ask you to prove it, do all the ninja business to do with rules of logs :ninja2:
    yeh i know that, but like you said i did it just incase they do ask to prove it, most likely not, but you never know what could come up in an exam.

    EDIT: i've seen them ask it in a paper i was doing, i'll try find out which it was again. but over the recent years they seem not to bother asking to prove it anymore. but yh you never know
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    (Original post by masryboy94)
    yeh i know that, but like you said i did it just incase they do ask to prove it, most likely not, but you never know what could come up in an exam.

    EDIT: i've seen them ask it in a paper i was doing, i'll try find out which it was again. but over the recent years they seem not to bother asking to prove it anymore. but yh you never know
    It could be asked in this reserve paper that we shall be sitting in less than a month, I would just prove it by using the formula provided for C3


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    (Original post by MathsNerd1)
    It could be asked in this reserve paper that we shall be sitting in less than a month, I would just prove it by using the formula provided for C3
    which formula is that?
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    (Original post by masryboy94)
    which formula is that?
    This one
    Name:  ImageUploadedByStudent Room1369782900.131823.jpg
Views: 79
Size:  156.9 KB


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    (Original post by fayled)
    I get the impression I could know everything I could ever know about maths, and still drop marks on a C4 paper because of some stupid arithmetical error.
    Just be extremely careful then
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    (Original post by MathsNerd1)
    This one
    Name:  ImageUploadedByStudent Room1369782900.131823.jpg
Views: 79
Size:  156.9 KB


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    how would you use it though? lool
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    (Original post by masryboy94)
    how would you use it though? lool
    To show a proof of dy/dx = a^xlna when y = a^x ?

    Just differentiate how you normally would and it very easily comes out to the required form


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    (Original post by MathsNerd1)
    To show a proof of dy/dx = a^xlna when y = a^x ?

    Just differentiate how you normally would and it very easily comes out to the required form


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    ooo, isn't that what i done in my previous post at the top of the page?
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    (Original post by masryboy94)
    ooo, isn't that what i done in my previous post at the top of the page?
    The way you've differentiated it is the C4 method that is included in the book, this method is slightly different but both work to get the same answer so just use whichever one you remember best I'm just too lazy to take the other approach as I'd rather just use the formula given


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    (Original post by MathsNerd1)
    The way you've differentiated it is the C4 method that is included in the book, this method is slightly different but both work to get the same answer so just use whichever one you remember best I'm just too lazy to take the other approach as I'd rather just use the formula given
    oo what way is it that you know? :rolleyes:
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    (Original post by masryboy94)
    oo what way is it that you know? :rolleyes:
    I'm not quite sure what you're asking, I'm just saying to derive a function to the power of x I just sub the variables into the formula provided in C3, but you can also do it in C4 way like you did at the top of the page, so it's really up to you in which method you choose


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    (Original post by MathsNerd1)
    I'm not quite sure what you're asking, I'm just saying to derive a function to the power of x I just sub the variables into the formula provided in C3, but you can also do it in C4 way like you did at the top of the page, so it's really up to you in which method you choose


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    yep got you now, loool sorry its past midnight, im abit tired haha :angelblush:
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    (Original post by masryboy94)
    yep got you now, loool sorry its past midnight, im abit tired haha :angelblush:
    That's understandabl then and yeah its rather late, but this is when I decide to get a few past papers complete
 
 
 
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