Results 1 to 5 of 5

Math Help - derivative of a trig function with 2 variables

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    12

    derivative of a trig function with 2 variables

    find dy/dx of sin(xy)=x+y

    So far I have

    cos(xy)*(xy'+1y)=1+y'
    (cos(xy))xy'+(cos(xy))y=1+y'

    Then, I'm sure you solve here for y but for the life of me I don't see the logical steps to get to y.

    Would it be

    y=((1+y')-(cos(xy)xy'))/(cos(xy))

    ???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by AlphaTauLambda View Post
    find dy/dx of sin(xy)=x+y

    So far I have

    cos(xy)*(xy'+1y)=1+y'
    (cos(xy))xy'+(cos(xy))y=1+y'

    Then, I'm sure you solve here for y but for the life of me I don't see the logical steps to get to y.

    Would it be

    y=((1+y')-(cos(xy)xy'))/(cos(xy))

    ???
    solve for y', which is dy/dx ... not y
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    12
    Skeeter. Thanks. I go to school in North Texas... haha

    The person who helped me with this problem has written (xcosxy-y)y'=1-ycosxy

    I don't understand the transition from the previous step (which is (cosxy)xy' + (cosxy)*y=1+y'

    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    \dfrac{d}{dx}\left[\sin(xy) = x+y]

    \cos(xy) \cdot (xy' + y) = 1 + y'

    distribute the \cos(xy) on the left ...

    xy'\cos(xy) + y\cos(xy) = 1 + y'

    get the terms w/ y' on the same side ...

    xy'\cos(xy) - y' = 1 - y\cos(xy)

    factor out y' ...

    y'[x\cos(xy) - 1] = 1 - y\cos(xy)

    y' = \dfrac{1 - y\cos(xy)}{x\cos(xy) - 1}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2011
    Posts
    12
    Thanks a million, Skeeter! This makes perfect sense!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derivative of this trig function
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 12th 2010, 01:55 PM
  2. trig function derivative
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 4th 2010, 07:00 AM
  3. Derivative of a function of two variables.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 11th 2009, 06:31 PM
  4. derivative of trig function
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 4th 2008, 08:07 PM
  5. Derivative of Trig Function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 28th 2008, 03:32 PM

Search Tags


/mathhelpforum @mathhelpforum