Results 1 to 2 of 2

Math Help - implicit differentiation... a very annoying question

  1. #1
    Member
    Joined
    Dec 2008
    From
    Australia
    Posts
    161

    Question implicit differentiation... a very annoying question

    If  x^2y = (x+y)^3
    show that dy/dx = y/x

    HOW??????

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by differentiate View Post
    If  x^2y = (x+y)^3
    show that dy/dx = y/x

    HOW??????

    Thanks

    Differentiating implicitly:

    2xydx+x^2dy=3(x+y)^2dx+3(x+y)^2dy\Longrightarrow(x  ^2-3(x+y)^2)dy=(3(x+y)^2-2xy)dx \Longrightarrow -(2x^2+6xy+3y^2)dy=(3x^2+4xy+3y^2)dx\Longrightarrow

     \frac{dy}{dx}=-\frac{3x^2+4xy+3y^2}{2x^2+6xy+3y^2}\neq \frac{y}{x} ...and thus the claim seems to be false.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Implicit Differentiation question
    Posted in the Calculus Forum
    Replies: 11
    Last Post: February 12th 2010, 02:18 AM
  2. another implicit differentiation question
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 6th 2010, 03:43 PM
  3. Implicit Differentiation Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 4th 2009, 04:34 AM
  4. Implicit Differentiation Question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 7th 2008, 06:08 AM
  5. Question about Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 23rd 2007, 09:34 PM

Search Tags


/mathhelpforum @mathhelpforum