Results 1 to 4 of 4

Math Help - Find dy/dx in terms of x and y

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    8

    Find dy/dx in terms of x and y

    Find dy/dx in terms of x and y for: xy = tan(xy)

    I'm not too good with this so pls dont skip steps pls.
    Last edited by mr fantastic; April 25th 2009 at 08:10 AM. Reason: Removed a careless mispelling that could lead to a misunderstanding.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2009
    Posts
    8
    anyways, i've gotten this far and need help

    xy=tan(xy)

    d(xy)/dx = d(tanxy)/dx

    x * dy/dx +y * dx/dx = sec^2(xy) * (d(xy)/dx)

    1 = sec^2(xy)

    1 = 1/(cos^2(xy))

    cos^2(xy) = 1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2009
    Posts
    166
    xy = tan(xy)

    xy' + y = sec^2(xy)(xy' + y) // chain rule

    xy' + y = sec^2(xy)xy' + sec^2(xy)y // expand

    xy' - sec^2(xy)xy' = sec^2(xy)y - y // move terms to opposite sides

    y'(1 - sec^2(xy)) = sec^2(xy)y - y // factor out y'

    y' = \frac {sec^2(xy)y - y}{1 - sec^2(xy)} // divide
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2009
    Posts
    8
    thanks!
    btw, x has been left out of the factorizing line.
    which when corrected, and factorised again after dividing, renders y' = -y/x
    thanks again!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find next two terms...
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 12th 2011, 11:33 AM
  2. Find a in terms of b
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: April 30th 2011, 08:38 PM
  3. Find u in terms of x from a given DE
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: June 28th 2010, 01:18 PM
  4. Find y in terms of x
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 13th 2009, 08:46 AM
  5. Find the first 5 terms
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 31st 2007, 06:02 PM

Search Tags


/mathhelpforum @mathhelpforum