Results 1 to 4 of 4

Math Help - implicit differentiation

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    22

    implicit differentiation

    Find all points on the curve
    x^2
    y^2+ xy = 2
    where the slope of the tangent line is -1.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by singh1030 View Post
    Find all points on the curve
    x^2
    y^2+ xy = 2
    where the slope of the tangent line is -1.
    do you mean x^2 + y^2 + xy = 2 ??
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2007
    Posts
    22
    yea i did sorry
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by singh1030 View Post
    yea i did sorry
    just remember to attach y' = dy/dx when you differentiate a y-term, since you are taking the derivative of y with respect to x. when we are taking the derivative of an x-term, we don't have to attach anything, since we would have dx/dx which cancels to 1. also note that we differentiate xy by the product rule

    x^2 + y^2 + xy = 2

    \Rightarrow 2x + 2y~y' + y + x~y' = 0

    we want the slope to be -1, so set y' = -1 and solve for the resulting function
    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