Results 1 to 6 of 6

Math Help - Double derivative of x^2/(1 + x)

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    3

    Double derivative of x^2/(1 + x)

    y=x^2/(1+x) Find the derivative of F"(1), By the " it means to find the double derivative, but I have no idea what to do, could anybody help me? thanks
    Last edited by mr fantastic; May 12th 2010 at 09:18 PM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    453
    Quote Originally Posted by timmehk View Post
    y=x^2/(1+x) Find the derivative of F"(1), By the " it means to find the double derivative, but I have no idea what to do, could anybody help me? thanks
    start by finding the first derivative ... can you do that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    3
    Ok I get 1/(1+x)^2 for the first derviative, but how do I solve for the second derivative? How can I use the quotient rule if I don't have an x in the numerator? Or, do I use the chain rule and disregard the fact that its division.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49
    Just in case a picture helps...



    ... shows the first derivative, where



    ... is the product rule, straight lines differentiating downwards. But,



    ... the chain rule, is involved - it hardly leaves a trace in this instance, but we can zoom in on it...



    Straight continuous lines still differentiate downwards with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Writing the bottom row with a common denominator...



    Then a similar routine to differentiate again...



    Spoiler:

    Then plug in 1 for x.

    Alternatively, you could use the quotient rule for differentiation (twice). But the pic can be useful as an overview of what's happening, and it means you don't need u and v.

    _________________________________________
    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    453
    Quote Originally Posted by timmehk View Post
    Ok I get 1/(1+x)^2 for the first derviative, but how do I solve for the second derivative? How can I use the quotient rule if I don't have an x in the numerator? Or, do I use the chain rule and disregard the fact that its division.
    your first derivative is incorrect.

    y = \frac{x^2}{1+x}

    quotient rule ...

    y' = \frac{(1+x)(2x) - (x^2)(1)}{(1+x)^2}<br />

    y' = \frac{2x + 2x^2 - x^2}{(1+x)^2}

    y' = \frac{2x+x^2}{(1+x)^2}

    to find the second derivative, quotient rule again ...

    y'' = \frac{(1+x)^2(2+2x) - (2x+x^2) \cdot 2(1+x)}{(1+x)^4}

    no need for simplification from this point ... since you only need to evaluate the second derivative at x = 1, just sub in 1 for x and do the arithmetic.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by timmehk View Post
    y=x^2/(1+x) Find the derivative of F"(1), By the " it means to find the double derivative, but I have no idea what to do, could anybody help me? thanks
    Note that \frac{x^2}{1 + x} = x - 1 + \frac{1}{x + 1} using polynomial long division. Getting the double derivative should now be a simple process.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof of double derivative.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 28th 2011, 06:34 AM
  2. tough double variable derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 2nd 2011, 06:08 AM
  3. Replies: 2
    Last Post: January 23rd 2010, 09:55 PM
  4. [SOLVED] Is this double derivative correct?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 20th 2009, 02:58 PM
  5. Integration of double derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 22nd 2008, 08:23 PM

Search Tags


/mathhelpforum @mathhelpforum