1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Directional derivative formula

  1. Oct 23, 2007 #1
    1. The problem statement, all variables and given/known data

    (Q) The derivative of f(x,y) at Po(1,2) in the direction i + j is 2sqrt(2) and in the direction of -2j is -3. What is the derivative of f in the direction of -i - 2j? Give reasons for your answers.

    2. Relevant equations

    The directional derivative is given by the formula:

    ∂f/∂x i+∂f/∂y j

    3. The attempt at a solution

    You get simultaneous equations when you apply the above equation and you find that

    ∂f/∂y = 3/2.
    And ∂f/∂x = [4sqrt(2) - 3] / 2.

    Then applying the dot product of this and -i - 2j, you get [-3-4sqrt(2)] / 2 but the answer is supposed to be -7/sqrt(5). How did they get that??:confused:
  2. jcsd
  3. Oct 23, 2007 #2


    User Avatar
    Science Advisor

    Yes, that's true.

    No, that's not true. "The derivative of f(x,y) at Po(1,2) in the direction i + j is 2sqrt(2)" tells you that [itex]f_x/\sqrt{2}+ f_y/\sqrt{2}= 2\sqrt{2}[/itex] (dividing by the length of i+ j) or that [itex]f_x+ f_y=4[/itex]. Since [itex]f_y= 3/2[/itex], that gives [itex]f_x= 5/2[/itex]

    No, take the dot product of [itex](5/2)i+ (3/2)j[/itex] with the unit vector in the direction of -i- 2j.

    Remember that the derivative in the direction of vector v is [itex]\nabla f \cdot v/||v||[/itex].

    You keep forgetting to divide by the length of v.
  4. Oct 23, 2007 #3
    Eye opener!!

    Thank-you very much for explicitly exposing my weakness!! I really mean it. Now, I'll never forget to divide by the length! :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook