Results 1 to 2 of 2

Math Help - Directional derivative and angles.

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    94

    Directional derivative and angles.

    Consider a surface S given by the equation z = f(x,y) where f(x,y)= xe^(4x^2-y^2).

    (a) Find the directional derivative Duf in the direction of u parallel to v = 3i+4j at the point A=(1,2).

    (b) Find the angles THETAx and THETAy of the directional vector u in (x,y) plane relative to x and y axes, respectively, at which the maxim of Duf at the point A is reached.

    For (a) I used the formula Duf(x,y) = Fx(x,y)cosTHETA + Fy(x,y)sinTHETA. I took the first order partial derivatives and plugged in the point A=(1,2). For THETA (and this is where I might have made a mistake) I used 3/4 because the directional derivative is parallel to v = 3i+4j.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    theta is arctan (4/3)

    To verify we can compute Df 2 ways using the formula you gave
    and the fact cos*arctan(4/3) = 3/5 and sin(arctan(4/3) =4/5

    Or we could use gradf*u where u is a unit vector since |3 i +4j| =5

    we have u = 3/5 i +4/5 j as before

    by the way the directional derivative is a number so it can't be parallel to u
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another Directional Derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 13th 2011, 12:42 PM
  2. Directional Derivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 17th 2010, 02:25 AM
  3. Directional derivative
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 10th 2009, 03:26 AM
  4. Total Derivative vs. Directional Derivative
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: May 30th 2008, 08:42 AM
  5. directional derivative
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 12th 2006, 04:39 AM

Search Tags


/mathhelpforum @mathhelpforum