1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Implicit Differentiation

  1. Jan 8, 2005 #1
    Hello all

    Given: x^2 + xy + y^2 - 7 = 0, solve for y using the quadratic forumula. Then find dy/dx at P(1,2) from a function of the form f(x).

    My solution:

    y = -x (+/-) sqrt( x^2 - 28) / 2.

    I am not sure if this is correct. After solving for y, do you have to implicitly take the derivative of y?
  2. jcsd
  3. Jan 8, 2005 #2
    you have to calculate the derivative with repsect to x of this given function. So just look at y as some function dependent on x ; so you have dy/dx...and dy²/dx = 2ydy/dx and so on...

    2x + y + xdy/dx + 2ydy/dx = 0

    you get this too ???

  4. Jan 8, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper

    [tex] y^{2}+xy+x^{2}-7=0 [/tex]
    Use the quadratic formula to find:
    [tex] y_{1,2}(x) =\frac{-x\pm\sqrt{28-3x^{2}}}{2} [/tex]
    The condition that the point (1,2) should be on the graph of "y" yields:
    [tex] y_{1}(1)=\frac{-1+\sqrt{28-3}}{2}=\frac{-1+5}{2}=2 [/tex](2)

    [tex] y_{2}(1)=\frac{-1-5}{2}=-3 [/tex] (3)

    So you need to chose the "+" sign from the explicitation.
    [tex] y(x)=\frac{1}{2}(\sqrt{28-3x^{2}}-x) [/tex]

    Compute its derivative and make "x=1" in the result.

    Last edited: Jan 8, 2005
  5. Jan 8, 2005 #4
    GUYS GUYS what are you doing...

    Your solution is NOT an implicit derivation. You don't need the quadratic formula at all. Besides the motivation, dextercioby for taken the + value is not correct.

    What you need to do is look at y as y(x) and calculate the derivative of the given formula with respect to x. This is the IMPLICIT part...the derivavtive that is asked is in a formula itself

    derivative with respect to x yields

    2x + y + x(dy/dx) + 2y(dy/dx) = 0


    [tex]\frac{dy}{dx} (x + 2y) = -(2x+y)[/tex]
    [tex]\frac{dy}{dx} = \frac{-2x-y}{x+2y}[/tex]

    Then fill in the given x and y values in the right hand side and all is done...

  6. Jan 8, 2005 #5
    how did you get 3x^2 for the term in the quadratic forumula dextercioby?

  7. Jan 8, 2005 #6


    User Avatar
    Science Advisor
    Homework Helper

    The discriminant is [itex] \Delta=b^{2}-4ac [/tex]
    Compute it,with [itex] a=1;b=x;c=x^{2}-7 [/itex]

  8. Jan 8, 2005 #7
    ok thanks alot
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Implicit Differentiation