Results 1 to 5 of 5

Math Help - implicit differentiation

  1. #1
    Senior Member
    Joined
    Apr 2009
    Posts
    253

    implicit differentiation

    Find \frac{d^2y}{dx^2} by implicit differentiation: 2x^3-3y^2=8

    So far I get
    \frac{dy}{dx}=\frac{x^2}{y}
    \frac{d^2y}{dx^2}=\frac{2y}{x} <----- incorrect


    correct answer= \frac{2xy^2-x^4}{y^3}

    How do i find the correct answer?
    Last edited by yoman360; September 12th 2009 at 01:49 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,888
    Thanks
    682
    Quote Originally Posted by yoman360 View Post
    Find \frac{d^2y}{dx^2} by implicit differentiation: 2x^3-3y^2=8
    show some effort ...

    what did you get for \frac{dy}{dx} ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Apr 2009
    Posts
    253
    I get \frac{dy}{dx}=\frac{x^2}{y}

    i keep getting the same answer

    this one is difficult
    Last edited by mr fantastic; September 12th 2009 at 03:10 PM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,888
    Thanks
    682
    2x^3-3y^2=8

    6x^2 - 6y \cdot y' = 0

    y' = \frac{x^2}{y}

    y'' = \frac{2xy - x^2y'}{y^2}

    y'' = \frac{2xy - \frac{x^4}{y}}{y^2}

    y'' = \frac{2xy^2 - x^4}{y^3}<br />
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2009
    Posts
    253
    Quote Originally Posted by skeeter View Post
    2x^3-3y^2=8

    6x^2 - 6y \cdot y' = 0

    y' = \frac{x^2}{y}

    y'' = \frac{2xy - x^2y'}{y^2}

    y'' = \frac{2xy - \frac{x^4}{y}}{y^2}

    y'' = \frac{2xy^2 - x^4}{y^3}<br />
    oh i see now I forgot to use the quotient rule
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 1st 2010, 07:42 AM
  3. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 28th 2010, 03:19 PM
  4. Implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 26th 2010, 05:41 PM
  5. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2008, 07:33 PM

Search Tags


/mathhelpforum @mathhelpforum