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    So we have the following expression, e^-2x / sqrt(x+1) Ive tried the quotient rule and the product rule but I can't seem to get the answer since there are so many terms and I don't knnow how to organise them
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    (Original post by Alex Dom)
    So we have the following expression, e^-2x / sqrt(x+1) Ive tried the quotient rule and the product rule but I can't seem to get the answer since there are so many terms and I don't knnow how to organise them
    Use the product rule as they are both two functions. The first function is e^-2x and the second being (x+1)^-1/2. Is that ok? Its important you understand it in case it came up in the exam.

    I missed a minus but it is the product rule and I have corrected it now ^
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    (Original post by Jackabc)
    Is that ok?
    No it isn't. Either your index is wrong or you mean the quotient rule.
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    (Original post by Alex Dom)
    So we have the following expression, e^-2x / sqrt(x+1) Ive tried the quotient rule and the product rule but I can't seem to get the answer since there are so many terms and I don't knnow how to organise them
    Either the product rule or the quotient rule will work. Care to share some working with us? It may just be that you have produced an equivalent correct answer that you don't know how to manipulate to the required form.
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    (Original post by Mr M)
    No it isn't. Either your index is wrong or you mean the quotient rule.
    Oh yeah I missed a minus lol. I always find it funny how mathematicians learn such advanced concepts and can forget something as simple as that.
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    (Original post by Mr M)
    Either the product rule or the quotient rule will work. Care to share some working with us? It may just be that you have produced an equivalent correct answer that you don't know how to manipulate to the required form.
    well I figured the quotient rule is easier to apply and got the following,

    [ -2x(sqrt(x+1)e^-2x] - [(-1/2) (x+1)^-3/2 (e^-2x)] all divided by x+1

    and then i Took out the common factor of e^-2x and then im stuck
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    (Original post by Alex Dom)
    well I figured the quotient rule is easier to apply and got the following,

    [ -2x(sqrt(x+1)e^-2x] - [(-1/2) (x+1)^-3/2 (e^-2x)] all divided by x+1

    and then i Took out the common factor of e^-2x and then im stuck
    The product rule is a lot easier

    (e^-2x)/sqrt(x+1)=(e^-2x)(x+1)^-1/2

    e^-2x[-0.5(x+1)^-3/2]+(x+1)^-1/2[-2e^-2x]

    Then simplify...

    Hint: Take out (x+1)^-3/2

    Or you can use the quotient rule, but that would take the piss.
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    (Original post by Alex Dom)
    well I figured the quotient rule is easier to apply and got the following,

    [ -2x(sqrt(x+1)e^-2x] - [(-1/2) (x+1)^-3/2 (e^-2x)] all divided by x+1

    and then i Took out the common factor of e^-2x and then im stuck
    That is terribly wrong.

    You have differentiated both terms incorrectly.

    \displaystyle \frac{d}{dx} e^{-2x} \neq -2x e^{-2x}

    \displaystyle \frac{d}{dx}(x+1)^{\frac{1}{2}} \neq -\frac{1}{2} (x+1)^{-\frac{3}{2}}
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    (Original post by Jackabc)
    The product rule is a lot easier

    (e^-2x)/sqrt(x+1)=(e^-2x)(x+1)^-1/2

    e^-2x[-0.5(x+1)^-3/2]+(x+1)^-1/2[-2e^-2x]

    Then simplify...

    Or you can use the quotient rule, but that would take the piss.
    The answer to the problem is - (4x+5)e^-2x all over 2(x+1)^3/2
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    (Original post by Mr M)
    That is terribly wrong.

    You have differentiated both terms incorrectly.

    \displaystyle \frac{d}{dx} e^{-2x} \neq -2x e^{-2x}

    \displaystyle \frac{d}{dx}(x+1)^{\frac{1}{2}} \neq -\frac{1}{2} (x+1)^{-\frac{3}{2}}
    oh god, let me do that again.
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    (Original post by Mr M)
    That is terribly wrong.

    You have differentiated both terms incorrectly.

    \displaystyle \frac{d}{dx} e^{-2x} \neq -2x e^{-2x}

    \displaystyle \frac{d}{dx}(x+1)^{\frac{1}{2}} \neq -\frac{1}{2} (x+1)^{-\frac{3}{2}}
    Well he was differentiating (x+1)^(-1/2) which was right
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    (Original post by Jackabc)
    Well he was differentiating (x+1)^(-1/2) which was right
    In that post he was doing the quotient rule, so it was (x+1)^(1/2).
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    (Original post by Jackabc)
    Well he was differentiating (x+1)^(-1/2) which was right
    I'm not sure you are helping. He clearly wasn't.

    (Original post by Alex Dom)
    well I figured the quotient rule is easier to apply and got the following
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    (Original post by Mr M)
    I'm not sure you are helping. He clearly wasn't.
    He was if you look below. The product rule works.

    The answer is here

    (Original post by Alex Dom)
    So we have the following expression, e^-2x / sqrt(x+1) Ive tried the quotient rule and the product rule but I can't seem to get the answer since there are so many terms and I don't knnow how to organise them
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    (Original post by Kerch)
    In that post he was doing the quotient rule, so it was (x+1)^(1/2).
    Oh yeah sorry, I am tired
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    (Original post by Jackabc)
    He was if you look below. The product rule works.

    The answer is here
    Well I suppose it is an appropriate time of year to teach your grandmother to suck eggs.
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    (Original post by Mr M)
    Well I suppose it is an appropriate time of year to teach your grandmother to suck eggs.
    Sorry Mr M. I guess you don't even see your grandmother seen as you spend a lot of your life making posts, not far to 20000 now.
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    (Original post by Jackabc)
    Sorry Mr M. I guess you don't even see your grandmother seen as you spend a lot of your life making posts, not far to 20000 now.
    They both died before I was born so that isn't a particularly cool thing to say. My top tip for the day is it is probably best not to neg people with massively higher rep power than you. Just as well I am not the vengeful sort!
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    (Original post by Mr M)
    They both died before I was born so that isn't a particularly cool thing to say. My top tip for the day is it is probably best not to neg people with massively higher rep power than you. Just as well I am not the vengeful sort!
    Oh no you just insult people in the first place but you aren't vengeful.
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    (Original post by Jackabc)
    you just insult people in the first place
    Eh?
 
 
 
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