Results 1 to 3 of 3

Math Help - Equation of tangent line to curve

  1. #1
    Member
    Joined
    Sep 2011
    Posts
    75

    Equation of tangent line to curve

    given:

    xy^\frac{1}{2} + yx^\frac{1}{2} = 6

    we are trying to find \frac{dy}{dx} so then, wouldn't you want to isolate y?

    eventually you want a m_2=\frac{1}{m_1}

    instead the book starts turning the original formula on this page into a derivative. I am in grants notes and have been stuck on this question for some time. If I work on it more I'll update this but if anyone thinks they can explain it, please do.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,646
    Thanks
    1596
    Awards
    1

    Re: Equation of tangent line to curve

    Quote Originally Posted by togo View Post
    given:
    xy^{\frac{1}{2}} + yx^{\frac{1}{2}} = 6

    we are trying to find \frac{dy}{dx}
    y^{\frac{1}{2}}+\frac{1}{2}xy^{-\frac{1}{2}}y'+x^{\frac{1}{2}}y'+\frac{1}{2}x^{-\frac{1}{2}}y=0

    Solve for y'.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: Equation of tangent line to curve

    Quote Originally Posted by togo View Post
    given:

    xy^\frac{1}{2} + yx^\frac{1}{2} = 6

    we are trying to find \frac{dy}{dx} so then, wouldn't you want to isolate y?
    Plato used a method called "implicit differentiation" where he did not need to isolate y.

    eventually you want a m_2=\frac{1}{m_1}

    instead the book starts turning the original formula on this page into a derivative. I am in grants notes and have been stuck on this question for some time. If I work on it more I'll update this but if anyone thinks they can explain it, please do.
    Yes, that's what "implicit differentiation" is. For example, differentiating " xy^2" with respect to x, you first use the product rule to say that is [tex](x)'y^2+ x(y^2)'[tex]. Of course, the derivative of x, with respect to x, is 1 and the derivative of y^2 with respect to x is, by the chain rule, the derivative of y^2 with respect to y times the derivative with respect to x: 2yy'. The is, the derivative of xy^2 with respect to x is (1)y^2+ x(2y)y'= y^2+ 2xyy'.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equation of the tangent line to the curve
    Posted in the Calculus Forum
    Replies: 11
    Last Post: August 9th 2010, 02:07 PM
  2. Equation for line tangent to curve
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 22nd 2009, 09:29 PM
  3. equation of the tangent line to the curve
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: November 16th 2008, 03:11 PM
  4. Equation of Line tangent to Curve.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 26th 2008, 10:24 PM
  5. Equation of tangent line to following curve.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 5th 2007, 10:45 AM

Search Tags


/mathhelpforum @mathhelpforum