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

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the Directional derivative of [tex]\varphi[/tex] = x2+siny-xz in the direction of i+2j-2k at the point (1, [tex]\pi[/tex]/2 , -3)

    3. The attempt at a solution

    u = i+2j-2k

    [tex]\left|[/tex]u[tex]\left|[/tex] = [tex]\sqrt{1^2+2^2+(-2)^2}[/tex] = 3


    [tex]\Rightarrow[/tex] u[tex]\hat{}[/tex] = 1/3i+2/3j-2/3k

    [tex]\nabla[/tex][tex]\varphi[/tex] = (2x-z)i+(Cos y)j-xk

    at the point (1, [tex]\pi[/tex]/2 , -3)
    u[tex]\hat{}[/tex][tex]\nabla[/tex][tex]\varphi[/tex] = 5/3 + 0 +2/3 = 7/3

    i think i have this right?
     
  2. jcsd
  3. Jan 31, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think you have it right.
     
  4. Jan 31, 2010 #3
    thanks a mill
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook