Results 1 to 11 of 11

Math Help - Directional derivative

  1. #1
    Junior Member
    Joined
    Aug 2008
    From
    USA
    Posts
    40

    Directional derivative

    Given

    F( x, y ,z) = 2x + 3y^2 + yz,

    find Directional derivative of F at ( 2 , -1, 5) along the direction given by line x = y = ( z / 2).

    -----------------------------------------------------------------------
    Directional derivative Formula = ∇f u

    i grad the F and achieve ( 2, 6y + z , y).

    then i sub ( 2 , -1, 5) which is the point into it <--- is this correct ?

    what is the u then ?

    many thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856
    Quote Originally Posted by Chris0724 View Post
    Given

    F( x, y ,z) = 2x + 3y^2 + yz,

    find Directional derivative of F at ( 2 , -1, 5) along the direction given by line x = y = ( z / 2).

    -----------------------------------------------------------------------
    Directional derivative Formula = ∇f u

    i grad the F and achieve ( 2, 6y + z , y).

    then i sub ( 2 , -1, 5) which is the point into it <--- is this correct ?

    what is the u then ?

    many thanks
    Yes, that is correct. u is the unit vector pointing in the given direction.

    However, there are two answers to this problem: just a line does not define a "direction". There are two unit vectors pointing along the "along" this line in opposite directions. The derivative in one direction is the negative of the derivative in the opposite direction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2008
    From
    USA
    Posts
    40
    Quote Originally Posted by HallsofIvy View Post
    However, there are two answers to this problem: just a line does not define a "direction". There are two unit vectors pointing along the "along" this line in opposite directions. The derivative in one direction is the negative of the derivative in the opposite direction.

    hi,

    i still have problem finding u. i don't know wat is the value of x , y , z...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Chris0724 View Post
    hi,

    i still have problem finding u. i don't know wat is the value of x , y , z...
    find it from the line. you were given the symmetric form of the equation of a line. can you find the direction vector for the line? the unit vector you want is in that direction
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Aug 2008
    From
    USA
    Posts
    40
    Quote Originally Posted by Jhevon View Post
    find it from the line. you were given the symmetric form of the equation of a line. can you find the direction vector for the line? the unit vector you want is in that direction

    oh i got it.... is it ( 1, 1, 0.5) ? Is that call the cartesian coordinate as well?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Chris0724 View Post
    oh i got it.... is it ( 1, 1, 0.5) ? Is that call the cartesian coordinate as well?
    no, that's not it.

    also, note that whatever vector you find, its negative will also work. this is what HallsofIvy meant by two answers.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Aug 2008
    From
    USA
    Posts
    40
    Quote Originally Posted by Jhevon View Post
    no, that's not it.

    also, note that whatever vector you find, its negative will also work. this is what HallsofIvy meant by two answers.
    so i will achieve ( 2, 6y + z , y) . [ ( 1, 1, 0.5) / |( 1, 1, 0.5)| ] ?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Chris0724 View Post
    so i will achieve ( 2, 6y + z , y) . [ ( 1, 1, 0.5) / |( 1, 1, 0.5)| ] ?
    no, your unit vector is wrong, i said that

    find the correct one then plug it into the formula you mentioned.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856
    No, Jhevon, his unit vector is right. It is (1, 1, 0.5) divided by its length and that is what he meant by "(1, 1, 0.5)/|(1, 1, 0.5)
    |.
    Chris0724, you can go ahead and put in the point (2, -1, 5) for x, y, and z.
    Last edited by HallsofIvy; March 15th 2009 at 03:39 PM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by HallsofIvy View Post
    No, Jhevon, his unit vector is right. It is (1, 1, 0.5) divided by its length and that is what he meant by "(1, 1, 0.5)/|(1, 1, 0.5)

    Chris0724, you can go ahead and put in the point (2, -1, 5) for x, y, and z.
    am i forgetting my calc 3? i would think that the direction vector for the line x = y = z/2 is <1,1,2> and so it should be <1,1,2>/|<1,1,2>|. maybe i'm drunk again
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,421
    Thanks
    1856
    Quote Originally Posted by Jhevon View Post
    am i forgetting my calc 3? i would think that the direction vector for the line x = y = z/2 is <1,1,2> and so it should be <1,1,2>/|<1,1,2>|. maybe i'm drunk again
    You are right and I am wrong. How foolish of me. Given x= y= z/2 and setting each to t, x= t, y= t, z= 2t are parametric equations and <1, 1, 2> is the vector.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. directional derivative q
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 28th 2009, 07:01 PM
  2. directional derivative Help
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 17th 2009, 10:42 PM
  3. Directional derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 18th 2008, 02:58 PM
  4. Total Derivative vs. Directional Derivative
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: May 30th 2008, 09:42 AM
  5. directional derivative
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 12th 2006, 05:39 AM

Search Tags


/mathhelpforum @mathhelpforum