Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Soroban

Thread: use explicit differentiation to find y prime (simple)

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    usa
    Posts
    23

    use explicit differentiation to find y prime (simple)

    $\displaystyle y = sin(3x+4y) $
    $\displaystyle y' = cos(3x+4y)(3+4y') $
    $\displaystyle \frac{y'}{3+4y'} = cos(3x+4y) $

    //please help me finish
    Last edited by rabert1; Apr 25th 2012 at 07:04 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848

    Re: use explicit differentiation to find y prime (simple)

    Hello, rabert1!

    $\displaystyle y \:=\: \sin(3x+4y) $

    $\displaystyle y' \:=\: \cos(3x+4y)\cdot (3+4y') $

    We have: . . . . . . $\displaystyle y' \;=\;(3+4y')\cos(3x+4y)$

    n . . . . . . . . . . . . $\displaystyle y' \;=\;3\cos(3x+4y) + 4y'\cos(3x+4y) $

    . . . $\displaystyle y' - 4y'\cis(3x+4y) \;=\;3\cos(3x+4y)$ . .
    Get the y' terms on one side.

    $\displaystyle y'\big[1 - 4\cos(3x+4y)\big] \;=\;3\cos(3x+4y)$ . .
    Factor.

    w . . . . . . . . . . . . $\displaystyle y' \;=\;\frac{3\cos(3x+4y)}{1 - 4\cos(3x+4y)}$
    Thanks from rabert1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Nov 25th 2010, 04:11 AM
  2. how to find explicit solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Sep 20th 2009, 07:36 PM
  3. Find an explicit particular solution
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: Jul 11th 2009, 12:32 PM
  4. [SOLVED] Differentiation in explicit form
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Jan 26th 2009, 02:19 AM
  5. find the explicit formula for sequence
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Sep 26th 2008, 04:24 PM

Search Tags


/mathhelpforum @mathhelpforum