Results 1 to 2 of 2

Math Help - Finding the tangent line

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Finding the tangent line

    (X^3)y + (x^2)y = 5xy find dy/dx @(2,5) and the equation of the tangent line.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    From
    United States
    Posts
    676
    Thanks
    19
    Quote Originally Posted by tigergirl View Post
    (X^3)y + (x^2)y = 5xy find dy/dx @(2,5) and the equation of the tangent line.
    You have to use implicit differentiation.

    yx^3+yx^2=5xy

    Apply the product rule to each term. Since each term is a product of two functions, the derivative will have 6 terms:

    (x^3\frac{dy}{dx}+3x^2y)+(\frac{dy}{dx}x^2+2xy)=5x  \frac{dy}{dx}+5y

    Now just do the algebra to solve for \frac{dy}{dx}. Then evaluate the derivative at that point. Just plug in the numbers (2,5) in the expression for the derivative. That will be the slope of your tangent line.

    The derivative I came up with looks like this:

    \frac{dy}{dx}=\frac{5y-3x^2y+2xy}{x^3+x^2-5x}

    Make sure you can get the same thing. Just plug in the x's and the y's. Then use the fact that the point (2,5) is on the line to wright the equation from y=mx+b
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  2. finding the tangent line
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 7th 2010, 11:07 PM
  3. Finding k of a Tangent Line
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 5th 2010, 03:46 AM
  4. finding a tangent line.......
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 9th 2009, 03:39 PM
  5. Finding a tangent line
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 12th 2009, 05:14 PM

Search Tags


/mathhelpforum @mathhelpforum