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Math Help - taking the second derivative of a rational function

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    taking the second derivative of a rational function

    Taking the second derivative of x/(x+1)^{4}


    for the first derivative I got

    1-3x/(x+1)^5

    the second derivative I'm not sure about. Im not even sure I did the first one correctly.


    thanks!
    Last edited by kingsolomonsgrave; November 1st 2012 at 06:17 PM.
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    Re: taking the second derivative of a rational function

    Quote Originally Posted by kingsolomonsgrave View Post
    Taking the second derivative of x/(x+1)^{4}


    for the first derivative I got

    ((x+1)^3-4x)/(p+1)^7

    the second derivative I'm not sure about. Im not even sure I did the first one correctly.


    thanks!


    No the first derivative is not correct.

    I am not a fan of the quotient rule, so I don't usually use it. Just use negative exponents to rewrite and use the product rule.

    x(x+1)^{-4}=(x+1)^{-4}-4x(x+1)^{-5}=(x+1)^{-5}((x+1)-4x)=\frac{-3x+1}{(x+1)^5}
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    Re: taking the second derivative of a rational function

    Quote Originally Posted by kingsolomonsgrave View Post
    Taking the second derivative of x/(x+1)^{4}
    Write it as y=x(x+1)^{-4}
    Then y'=(x+1)^{-4}+x[-4(x+1)^{-5}]

    What is next?
    Last edited by Plato; November 2nd 2012 at 05:37 AM.
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    Re: taking the second derivative of a rational function

    Quote Originally Posted by kingsolomonsgrave View Post
    Taking the second derivative of x/(x+1)^{4}


    for the first derivative I got

    1-3x/(x+1)^5

    the second derivative I'm not sure about. Im not even sure I did the first one correctly.


    thanks!
    Your first derivative is correct, though you should write it properly as
    f'(x) = \frac{-3x + 1}{(x + 1)^5}

    So now do your quotient rule again:
    f''(x) = \frac{(-3)(x + 1)^5 - (-3x + 1)*5(x + 1)^4}{(x + 1)^{10}}

    -Dan

    FYI By order of operations
    1 -3x / (x + 1)^5 = 1 - \frac{3x}{(x + 1)^5}
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    Re: taking the second derivative of a rational function

    Hi Plato, there is a small (probably typing error) in your answer for f'.

    Salahuddin
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