Results 1 to 2 of 2

Math Help - xsin(y) = cos(x+y) , then find y'

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    13

    xsin(y) = cos(x+y) , then find y'

    Ive been banging my head on this one for 30 minutes..

    xsin(y) = cos(x+y) , then find y'
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2010
    Posts
    354
    Quote Originally Posted by alny View Post
    Ive been banging my head on this one for 30 minutes..

    xsin(y) = cos(x+y) , then find y'
    \frac{d}{dx} (x \sin y) = \frac{d}{dx} \cos(x+y)

    First, the left side using the product rule:

    \frac{d}{dx} (x \sin y) = \frac{d}{dx} (x) \cdot \sin y + x \cdot \frac{d}{dx} (\sin y) = \sin y + x \cos y \, \frac{dy}{dx}

    Now the other side:

    \frac{d}{dx} \cos(x+y) = -\sin(x+y) \cdot \frac{d}{dx} (x+y) = -\sin(x+y) \cdot \left(1+\frac{dy}{dx}\right)

    So we now have:

    \sin y + x \cos y \, \frac{dy}{dx} = -\sin(x+y) \cdot \left(1+\frac{dy}{dx}\right)

    At this point is it an algebra problem to solve for \frac{dy}{dx}. Can you finish this?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 22nd 2011, 05:57 PM
  2. Replies: 2
    Last Post: July 5th 2010, 09:48 PM
  3. xsin^-1 x
    Posted in the Calculus Forum
    Replies: 11
    Last Post: September 20th 2009, 03:57 PM
  4. Replies: 0
    Last Post: June 16th 2009, 01:43 PM
  5. Integral xsin^2(x)cos(x)ds
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 4th 2008, 07:30 PM

Search Tags


/mathhelpforum @mathhelpforum