Results 1 to 7 of 7

Math Help - derivative

  1. #1
    Member
    Joined
    Oct 2007
    From
    Nevada
    Posts
    188

    derivative

    Find the value(s) of dy/dx for x^2 * y + y^2 = 5 at y =1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,408
    What are you having trouble with? Differentiate both sides with respect to x and solve for y'. Find the cooresponding x coordinate (since you have y = 1) and plug it in to your expression for y' (it'll contain x's and y's).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2007
    From
    Nevada
    Posts
    188
    isn't there something tricky when differentiating y's? tahts what bugs me
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2007
    Posts
    144
    x^2y+y^2~=~5

    Tackle this in parts;
    Firstly use the product rule.

    Let u=x^2~,~v=y

    \frac{du}{dx}~=~2x~,~\frac{dv}{dx}~=~\frac{dy}{dx}

    \frac{d}{dx}(x^2y)~=~x^2\frac{dy}{dx}+2xy

    \implies~\frac{d}{dx}(x^2y+y^2~=~5)~\implies~x^2\f  rac{dy}{dx}+2xy+2y\frac{dy}{dx}~=~0

    \implies~\frac{dy}{dx}(x^2+2y)~=~-2xy

     <br />
\implies~\frac{dy}{dx}~=~\frac{-2xy}{x^2+2y}<br />

    Then substitute your y-value and x-value (which you can calculate using the given formula)

    Just like o_O said
    Last edited by Sean12345; April 15th 2008 at 09:46 AM. Reason: mistake
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2007
    Posts
    144
    In case you were wondering i got -\frac{2}{3}
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2007
    From
    Nevada
    Posts
    188
    why can't it be positive 2/3 as well?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Aug 2007
    Posts
    144
    Quote Originally Posted by DINOCALC09 View Post
    why can't it be positive 2/3 as well?
    It can be i just took x to be positive.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 03:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 12:40 PM
  3. Replies: 2
    Last Post: November 6th 2009, 03:51 PM
  4. Replies: 1
    Last Post: January 7th 2009, 02:59 PM
  5. Fréchet derivative and Gâteaux derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 23rd 2008, 05:40 PM

Search Tags


/mathhelpforum @mathhelpforum