Results 1 to 4 of 4

Math Help - implicit differentiation

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    53

    implicit differentiation

    Given:
    ye^y=(x-5y)^3

    Find \frac{dy}{dx}, in terms of x and y.

    what I tried to do was

    Differentiate implicitly wrt x,
    \frac{dy}{dx}(e^y)+\frac{dy}{dx}(y)(e^y)=(3)(x-5y)^2(1-5\frac{dy}{dx})
    \frac{dy}{dx}(e^y)(1+y)=3(x-5y)^2(1-5\frac{dy}{dx})

    then, i'm stuck in moving all \frac{dy}{dx} to the left-hand side.
    any help is much appreciated. thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: implicit differentiation

    Quote Originally Posted by wintersoltice View Post
    Given:
    ye^y=(x-5y)^3

    Find \frac{dy}{dx}, in terms of x and y.

    what I tried to do was

    Differentiate implicitly wrt x,
    \frac{dy}{dx}(e^y)+\frac{dy}{dx}(y)(e^y)=(3)(x-5y)^2(1-5\frac{dy}{dx})
    \frac{dy}{dx}(e^y)(1+y)=3(x-5y)^2(1-5\frac{dy}{dx})

    then, i'm stuck in moving all \frac{dy}{dx} to the left-hand side.
    any help is much appreciated. thanks.
    \frac{dy}{dx}(e^y)(1+y)=3(x-5y)^2-15\frac{dy}{dx}(x-5y)^2

    \frac{dy}{dx}[e^y(1+y)+15(x-5y)^2]=3(x-5y)^2

    \frac{dy}{dx}=\frac{3(x-5y)^2}{e^y(1+y)+15(x-5y)^2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2008
    Posts
    53

    Re: implicit differentiation

    Quote Originally Posted by alexmahone View Post
    \frac{dy}{dx}(e^y)(1+y)=3(x-5y)^2-15\frac{dy}{dx}(x-5y)^2

    \frac{dy}{dx}[e^y(1+y)+15(x-5y)^2]=3(x-5y)^2

    \frac{dy}{dx}=\frac{3(x-5y)^2}{e^y(1+y)+15(x-5y)^2}
    how did (1-5\frac{dy}{dx})
    become -15\frac{dy}{dx}(x-5y)^2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: implicit differentiation

    Quote Originally Posted by wintersoltice View Post
    how did (1-5\frac{dy}{dx})
    become -15\frac{dy}{dx}(x-5y)^2?
    3(1-5\frac{dy}{dx})=3-15\frac{dy}{dx}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. implicit differentiation
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 25th 2010, 01:40 PM
  3. implicit differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 13th 2010, 09:23 PM
  4. implicit differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 12th 2009, 03:15 PM
  5. A different implicit differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 19th 2008, 10:21 PM

Search Tags


/mathhelpforum @mathhelpforum